The Database of Integer Sequences, Part 0 

     Part of the On-Line Encyclopedia of Integer Sequences


This is a section of the main database for the On-Line Encyclopedia of Integer Sequences.

For more information see the following pages:
( www.research.att.com/~njas/sequences/ then )

    Seis.html:          Welcome
    index.html:         Lookup 
    indexfr.html:       Francais
    demo1.html:         Demos 
    Sindx.html:         Index 
    WebCam.html:        WebCam
    Submit.html:        Contribute new sequence or comment 
    eishelp1.html:      Internal format 
    eishelp2.html:      Beautified format
    transforms.html:    Transforms 
    Spuzzle.html:       Puzzles 
    Shot.html:          Hot 
    classic.html:       Classics
    ol.html:            Superseeker 
    JIS/index.html:     Journal of Integer Sequences
    pages.html:         More pages 

Maintained  by:         N. J. A. Sloane (njas@research.att.com), 
    home page:          www.research.att.com/~njas/
    


(start)



%I A000004
%S A000004 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T A000004 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U A000004 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A000004 The zero sequence.
%H A000004 N. J. A. Sloane, <a href="http://www.research.att.com/~njas/sequences/b000004.txt">Table of n, a(n) for n = 0..1000</a> [Useful when plotting one sequence against another. See Swayne link.]
%H A000004 D. F. Swayne, <a href="http://www.research.att.com/~njas/sequences/plot2.html">Plot pairs of sequences in the OEIS</a>
%H A000004 <a href="http://www.research.att.com/~njas/sequences/Sindx_Cor.html#core">Index entries for "core" sequences</a>
%p A000004 A000004 := n->0;
%t A000004 a[ n_ ] := 0
%o A000004 (MAGMA) [ 0 : n in [0..100]];
%o A000004 (PARI) vector(100,n,0)
%Y A000004 Cf. A000012, A007395, A010701.
%Y A000004 Adjacent sequences: A000001 A000002 A000003 this_sequence A000005 A000006 A000007
%Y A000004 Sequence in context: this_sequence A112316 A023976 A025469
%K A000004 core,easy,nonn,mult
%O A000004 0,1
%A A000004 njas

%I A112316
%S A112316 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T A112316 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
%U A112316 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0
%N A112316 Number of partitions of n into products of 6 primes.
%e A112316 a(160) = 2 since 160 = 96+64.
%Y A112316 Cf. A046306, A000607, A101049, A112313, A112314, A112315.
%Y A112316 Adjacent sequences: A112313 A112314 A112315 this_sequence A112317 A112318 A112319
%Y A112316 Sequence in context: A000004 this_sequence A023976 A025469 A025466
%K A112316 nonn
%O A112316 1,1
%A A112316 Jonathan Vos Post (jvospost2(AT)yahoo.com) and Ray Chandler (rayjchandler(AT)sbcglobal.net), Sep 02 2005

%I A023976
%S A023976 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T A023976 0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%U A023976 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%N A023976 First bit in fractional part of binary expansion of 9-th root of n.
%t A023976 Array[Function[n, RealDigits[N[Power[n, 1/9 ], 10 ], 2 ]// (#[[1, #[[2 ] ]+1 ] ])& ], 110 ]
%Y A023976 Adjacent sequences: A023973 A023974 A023975 this_sequence A023977 A023978 A023979
%Y A023976 Sequence in context: A000004 A112316 this_sequence A025469 A025466 A072769
%K A023976 nonn,base
%O A023976 1,1
%A A023976 njas, Olivier Gerard (ogerard(AT)ext.jussieu.fr)

%I A025469
%S A025469 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T A025469 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U A025469 0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0
%N A025469 Number of partitions of n into 3 distinct positive cubes.
%Y A025469 Adjacent sequences: A025466 A025467 A025468 this_sequence A025470 A025471 A025472
%Y A025469 Sequence in context: A000004 A112316 A023976 this_sequence A025466 A072769 A070204
%K A025469 nonn
%O A025469 0,1
%A A025469 David W. Wilson (davidwwilson(AT)comcast.net)

%I A025466
%S A025466 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T A025466 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U A025466 0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0
%N A025466 Number of partitions of n into 4 distinct nonnegative cubes.
%Y A025466 Adjacent sequences: A025463 A025464 A025465 this_sequence A025467 A025468 A025469
%Y A025466 Sequence in context: A112316 A023976 A025469 this_sequence A072769 A070204 A011745
%K A025466 nonn
%O A025466 0,1
%A A025466 David W. Wilson (davidwwilson(AT)comcast.net)

%I A072769
%S A072769 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,
%T A072769 0,0,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0,0,0,1,0,1,0,0,0,1,0,
%U A072769 1,0,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0
%V A072769 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,
%W A072769 0,0,1,0,1,0,0,0,0,0,0,1,0,-1,0,1,0,0,0,0,0,1,0,-1,0,-1,0,1,0,0,0,0,1,0,-1,0,0,0,-1,0,
%X A072769 1,0,0,0,1,0,-1,0,0,1,0,0,-1,0,1,0,0,1,0,-1,0,0,1,0,1,0,0,-1,0,1,0,1,0,-1,0,0,1,0
%N A072769 Differences between A071673 and A072768.
%C A072769 The term a(0) = A071673(0)-A072768(0) = 0-0 = 0 is not explicitly listed here as to get a better looking triangle.
%o A072769 (Scheme) (define (A072769 n) (- (A071673 n) (A072768 n)))
%Y A072769 Adjacent sequences: A072766 A072767 A072768 this_sequence A072770 A072771 A072772
%Y A072769 Sequence in context: A023976 A025469 A025466 this_sequence A070204 A011745 A011744
%K A072769 sign,tabl
%O A072769 1,1
%A A072769 Antti Karttunen Jun 12 2002

%I A070204
%S A070204 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,
%T A070204 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
%U A070204 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A070204 Number of isosceles integer triangles with perimeter n having integral inradius.
%C A070204 a(n) = A070201(n) - A070203(n).
%H A070204 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Incircle.html">Incircle</a>.
%H A070204 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/IsoscelesTriangle.html">Isosceles Triangle</a>.
%H A070204 R. Zumkeller, <a href="http://www.research.att.com/~njas/sequences/a070080.txt">Integer-sided triangles</a>
%Y A070204 Cf. A070139, A059169.
%Y A070204 Adjacent sequences: A070201 A070202 A070203 this_sequence A070205 A070206 A070207
%Y A070204 Sequence in context: A025469 A025466 A072769 this_sequence A011745 A011744 A011743
%K A070204 nonn
%O A070204 1,1
%A A070204 Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), May 05 2002

%I A011745
%S A011745 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T A011745 0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%U A011745 1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0
%N A011745 A binary m-sequence: expansion of reciprocal of x^32+x^28+x^27+x+1.
%D A011745 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011745 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011745 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011745 Adjacent sequences: A011742 A011743 A011744 this_sequence A011746 A011747 A011748
%Y A011745 Sequence in context: A025466 A072769 A070204 this_sequence A011744 A011743 A011742
%K A011745 nonn
%O A011745 0,1
%A A011745 njas

%I A011744
%S A011744 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T A011744 0,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,
%U A011744 1,0,0,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0
%N A011744 A binary m-sequence: expansion of reciprocal of x^31+x^3+1.
%D A011744 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011744 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011744 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011744 Adjacent sequences: A011741 A011742 A011743 this_sequence A011745 A011746 A011747
%Y A011744 Sequence in context: A072769 A070204 A011745 this_sequence A011743 A011742 A011741
%K A011744 nonn
%O A011744 0,1
%A A011744 njas

%I A011743
%S A011743 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T A011743 0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,
%U A011743 0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0
%N A011743 A binary m-sequence: expansion of reciprocal of x^30+x^16+x^15+x+1.
%D A011743 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011743 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011743 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011743 Adjacent sequences: A011740 A011741 A011742 this_sequence A011744 A011745 A011746
%Y A011743 Sequence in context: A070204 A011745 A011744 this_sequence A011742 A011741 A011740
%K A011743 nonn
%O A011743 0,1
%A A011743 njas

%I A011742
%S A011742 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T A011742 0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,
%U A011742 1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,1
%N A011742 A binary m-sequence: expansion of reciprocal of x^29+x^2+1.
%D A011742 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011742 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011742 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011742 Adjacent sequences: A011739 A011740 A011741 this_sequence A011743 A011744 A011745
%Y A011742 Sequence in context: A011745 A011744 A011743 this_sequence A011741 A011740 A085974
%K A011742 nonn
%O A011742 0,1
%A A011742 njas

%I A011741
%S A011741 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T A011741 1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,
%U A011741 1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0
%N A011741 A binary m-sequence: expansion of reciprocal of x^28+x^3+1.
%D A011741 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011741 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011741 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011741 Adjacent sequences: A011738 A011739 A011740 this_sequence A011742 A011743 A011744
%Y A011741 Sequence in context: A011744 A011743 A011742 this_sequence A011740 A085974 A011739
%K A011741 nonn
%O A011741 0,1
%A A011741 njas

%I A011740
%S A011740 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,
%T A011740 1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,
%U A011740 1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,1
%N A011740 A binary m-sequence: expansion of reciprocal of x^27+x^8+x^7+x+1.
%D A011740 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011740 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011740 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011740 Adjacent sequences: A011737 A011738 A011739 this_sequence A011741 A011742 A011743
%Y A011740 Sequence in context: A011743 A011742 A011741 this_sequence A085974 A011739 A023975
%K A011740 nonn
%O A011740 0,1
%A A011740 njas

%I A085974
%S A085974 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0,
%T A085974 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,
%U A085974 0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0
%N A085974 Number of 0's in decimal expansion of prime(n).
%e A085974 prime(26) = 101, so a(26)=1 and prime(1230) = 10007, so
%e A085974 a(1230)=3.
%Y A085974 Cf. 1's A085975, 2's A085976, 3's A085977, 4's A085978, 5's A085979, 6's A085980, 7's A085981, 8's A085982, 9's A085983.
%Y A085974 Adjacent sequences: A085971 A085972 A085973 this_sequence A085975 A085976 A085977
%Y A085974 Sequence in context: A011742 A011741 A011740 this_sequence A011739 A023975 A011738
%K A085974 base,nonn
%O A085974 1,1
%A A085974 Jason Earls (jcearls(AT)cableone.net), Jul 06 2003

%I A011739
%S A011739 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,
%T A011739 1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,
%U A011739 1,0,1,0,1,0,0,1,0,1,0,0,0,1,1,1,1,1,1,1,0,0,0,1,1,1,0
%N A011739 A binary m-sequence: expansion of reciprocal of x^26+x^8+x^7+x+1.
%D A011739 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011739 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011739 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011739 Adjacent sequences: A011736 A011737 A011738 this_sequence A011740 A011741 A011742
%Y A011739 Sequence in context: A011741 A011740 A085974 this_sequence A023975 A011738 A011737
%K A011739 nonn
%O A011739 0,1
%A A011739 njas

%I A023975
%S A023975 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,
%T A023975 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%U A023975 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%N A023975 First bit in fractional part of binary expansion of 8-th root of n.
%t A023975 Array[ Function[ n, RealDigits[ N[ Power[ n, 1/8 ], 10 ], 2 ]// (#[ [ 1, #[ [ 2 ] ]+1 ] ])& ], 110 ]
%Y A023975 Adjacent sequences: A023972 A023973 A023974 this_sequence A023976 A023977 A023978
%Y A023975 Sequence in context: A011740 A085974 A011739 this_sequence A011738 A011737 A076142
%K A023975 nonn,base
%O A023975 1,1
%A A023975 njas, Olivier Gerard (ogerard(AT)ext.jussieu.fr)

%I A011738
%S A011738 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,
%T A011738 1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,
%U A011738 1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,1,0,1,1,1,0
%N A011738 A binary m-sequence: expansion of reciprocal of x^25+x^3+1.
%D A011738 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011738 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011738 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011738 Adjacent sequences: A011735 A011736 A011737 this_sequence A011739 A011740 A011741
%Y A011738 Sequence in context: A085974 A011739 A023975 this_sequence A011737 A076142 A011736
%K A011738 nonn
%O A011738 0,1
%A A011738 njas

%I A011737
%S A011737 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,
%T A011737 0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0,0,1,0,1,
%U A011737 1,1,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,0,1,1,1,1,0,1,1
%N A011737 A binary m-sequence: expansion of reciprocal of x^24+x^4+x^3+x+1.
%D A011737 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011737 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011737 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011737 Adjacent sequences: A011734 A011735 A011736 this_sequence A011738 A011739 A011740
%Y A011737 Sequence in context: A011739 A023975 A011738 this_sequence A076142 A011736 A085982
%K A011737 nonn
%O A011737 0,1
%A A011737 njas

%I A076142
%S A076142 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,
%T A076142 0,0,0,0,0,0,0,1,0,0,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,1,1,0,1,0,
%U A076142 0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,0,0,0,0,1,0,1,0,0,0,1,1,0
%N A076142 a(n) = A064097(n) - A003313(n).
%F A076142 It seems that sum(k = 1, n, a(k)) * ln(n)/n^2 -> c (0.006 <c<0.01).
%Y A076142 Cf. A076091.
%Y A076142 Adjacent sequences: A076139 A076140 A076141 this_sequence A076143 A076144 A076145
%Y A076142 Sequence in context: A023975 A011738 A011737 this_sequence A011736 A085982 A011735
%K A076142 nonn
%O A076142 1,1
%A A076142 Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 31 2002

%I A011736
%S A011736 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,
%T A011736 1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,1,0,1,0,0,0,0,1,0,
%U A011736 0,1,0,1,0,0,0,0,1,0,0,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0,0
%N A011736 A binary m-sequence: expansion of reciprocal of x^23+x^5+1.
%D A011736 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011736 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011736 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011736 Adjacent sequences: A011733 A011734 A011735 this_sequence A011737 A011738 A011739
%Y A011736 Sequence in context: A011738 A011737 A076142 this_sequence A085982 A011735 A011734
%K A011736 nonn
%O A011736 0,1
%A A011736 njas

%I A085982
%S A085982 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,
%T A085982 0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,
%U A085982 0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0
%N A085982 Number of 8's in decimal expansion of prime(n).
%Y A085982 Cf. 0's A085974, 1's A085975, 2's A085976, 3's A085977, 4's A085978, 5's A085979, 6's A085980, 7's A085981, 9's A085983.
%Y A085982 Adjacent sequences: A085979 A085980 A085981 this_sequence A085983 A085984 A085985
%Y A085982 Sequence in context: A011737 A076142 A011736 this_sequence A011735 A011734 A011733
%K A085982 base,nonn
%O A085982 1,1
%A A085982 Jason Earls (jcearls(AT)cableone.net), Jul 06 2003

%I A011735
%S A011735 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,
%T A011735 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,
%U A011735 1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1
%N A011735 A binary m-sequence: expansion of reciprocal of x^22+x+1.
%D A011735 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011735 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011735 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011735 Adjacent sequences: A011732 A011733 A011734 this_sequence A011736 A011737 A011738
%Y A011735 Sequence in context: A076142 A011736 A085982 this_sequence A011734 A011733 A011732
%K A011735 nonn
%O A011735 0,1
%A A011735 njas

%I A011734
%S A011734 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,0,1,
%T A011734 0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,
%U A011734 1,0,1,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0
%N A011734 A binary m-sequence: expansion of reciprocal of x^21+x^2+1.
%D A011734 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011734 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011734 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011734 Adjacent sequences: A011731 A011732 A011733 this_sequence A011735 A011736 A011737
%Y A011734 Sequence in context: A011736 A085982 A011735 this_sequence A011733 A011732 A011731
%K A011734 nonn
%O A011734 0,1
%A A011734 njas

%I A011733
%S A011733 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,
%T A011733 0,1,0,0,1,0,0,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,
%U A011733 0,1,0,1,1,1,0,1,1,1,1,0,0,1,0,1,1,1,0,1,1,1,1,0,0,0,0
%N A011733 A binary m-sequence: expansion of reciprocal of x^20+x^3+1.
%D A011733 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011733 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011733 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011733 Adjacent sequences: A011730 A011731 A011732 this_sequence A011734 A011735 A011736
%Y A011733 Sequence in context: A085982 A011735 A011734 this_sequence A011732 A011731 A085980
%K A011733 nonn
%O A011733 0,1
%A A011733 njas

%I A011732
%S A011732 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,
%T A011732 0,1,1,1,1,1,0,0,0,0,1,1,0,1,0,1,1,0,1,0,0,1,1,1,1,1,0,
%U A011732 0,0,1,0,1,0,0,0,0,1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0,1,1
%N A011732 A binary m-sequence: expansion of reciprocal of x^19+x^6+x^5+x+1.
%D A011732 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011732 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011732 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011732 Adjacent sequences: A011729 A011730 A011731 this_sequence A011733 A011734 A011735
%Y A011732 Sequence in context: A011735 A011734 A011733 this_sequence A011731 A085980 A023974
%K A011732 nonn
%O A011732 0,1
%A A011732 njas

%I A011731
%S A011731 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,
%T A011731 0,0,0,0,1,0,0,0,1,0,0,1,0,0,0,0,0,0,1,0,0,0,1,0,0,1,1,
%U A011731 0,0,0,0,0,1,1,0,0,1,0,0,1,0,0,0,0,1,0,1,0,0,0,1,0,0,1
%N A011731 A binary m-sequence: expansion of reciprocal of x^18+x^7+1.
%D A011731 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011731 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011731 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011731 Adjacent sequences: A011728 A011729 A011730 this_sequence A011732 A011733 A011734
%Y A011731 Sequence in context: A011734 A011733 A011732 this_sequence A085980 A023974 A011730
%K A011731 nonn
%O A011731 0,1
%A A011731 njas

%I A085980
%S A085980 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T A085980 0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U A085980 0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,1,0
%N A085980 Number of 6's in decimal expansion of prime(n).
%Y A085980 Cf. 0's A085974, 1's A085975, 2's A085976, 3's A085977, 4's A085978, 5's A085979, 7's A085981, 8's A085982, 9's A085983.
%Y A085980 Adjacent sequences: A085977 A085978 A085979 this_sequence A085981 A085982 A085983
%Y A085980 Sequence in context: A011733 A011732 A011731 this_sequence A023974 A011730 A101637
%K A085980 base,nonn
%O A085980 1,1
%A A085980 Jason Earls (jcearls(AT)cableone.net), Jul 06 2003

%I A023974
%S A023974 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%T A023974 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%U A023974 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%N A023974 First bit in fractional part of binary expansion of 7-th root of n.
%t A023974 Array[ Function[ n, RealDigits[ N[ Power[ n, 1/7 ], 10 ], 2 ]// (#[ [ 1, #[ [ 2 ] ]+1 ] ])& ], 110 ]
%Y A023974 Adjacent sequences: A023971 A023972 A023973 this_sequence A023975 A023976 A023977
%Y A023974 Sequence in context: A011732 A011731 A085980 this_sequence A011730 A101637 A011729
%K A023974 nonn,base
%O A023974 1,1
%A A023974 njas, Olivier Gerard (ogerard(AT)ext.jussieu.fr)

%I A011730
%S A011730 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,0,1,0,
%T A011730 0,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,1,1,
%U A011730 0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,1,1,0,0,1,1,1,1,1,0,0,0
%N A011730 A binary m-sequence: expansion of reciprocal of x^17+x^3+1.
%D A011730 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011730 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011730 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011730 Adjacent sequences: A011727 A011728 A011729 this_sequence A011731 A011732 A011733
%Y A011730 Sequence in context: A011731 A085980 A023974 this_sequence A101637 A011729 A011728
%K A011730 nonn
%O A011730 0,1
%A A011730 njas

%I A101637
%S A101637 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,
%T A101637 1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
%U A101637 0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,1
%N A101637 a(n) = 1 iff n is a 4-almost prime, else 0.
%C A101637 See A101638 for the inverse Moebius transform of this sequence. 4-almost primes are a generalization of primes and semiprimes. Each 4-almost primes is the product of two (not necessarily distinct) semiprimes. As explained in Weisstein: "The primes correspond to the "1-almost prime" numbers 2, 3, 5, 7, 11, ... (A000040). The 2-almost prime numbers correspond to semiprimes 4, 6, 9, 10, 14, 15, 21, 22, ... (A001358). The first few 3-almost primes are 8, 12, 18, 20, 27, 28, 30, 42, 44, 45, 50, 52, 63, 66, 68, 70, 75, 76, 78, 92, 98, 99, ... (A014612). The first few 4-almost primes are 16, 24, 36, 40, 54, 56, 60, 81, 84, 88, 90, 100, ... (A014613). The first few 5-almost primes are 32, 48, 72, 80, ... (A014614)."
%H A101637 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Almostprime.html">Almost Prime.</a>
%e A101637 a(100) = 1 because 100 = 2 * 2 * 5 * 5 is the product of exactly 4 primes and thus is a 4-almost prime.
%Y A101637 Cf. A101638, A014613, A000040, A001358, A014612, A014614.
%Y A101637 Adjacent sequences: A101634 A101635 A101636 this_sequence A101638 A101639 A101640
%Y A101637 Sequence in context: A085980 A023974 A011730 this_sequence A011729 A011728 A133010
%K A101637 easy,nonn
%O A101637 1,1
%A A101637 Jonathan Vos Post (jvospost2(AT)yahoo.com), Dec 10 2004

%I A011729
%S A011729 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,1,0,1,0,0,0,0,
%T A011729 1,0,1,1,0,1,0,1,1,0,1,0,0,0,0,1,1,1,1,1,1,0,1,1,1,1,1,
%U A011729 1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0,1,1,0,0,1,0,0,0,0,0
%N A011729 A binary m-sequence: expansion of reciprocal of x^16+x^5+x^3+x^2+1.
%D A011729 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011729 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011729 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011729 Adjacent sequences: A011726 A011727 A011728 this_sequence A011730 A011731 A011732
%Y A011729 Sequence in context: A023974 A011730 A101637 this_sequence A011728 A133010 A071031
%K A011729 nonn
%O A011729 0,1
%A A011729 njas

%I A011728
%S A011728 0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,
%T A011728 1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,
%U A011728 1,0,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,0
%N A011728 A binary m-sequence: expansion of reciprocal of x^15+x+1.
%D A011728 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011728 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011728 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011728 Adjacent sequences: A011725 A011726 A011727 this_sequence A011729 A011730 A011731
%Y A011728 Sequence in context: A011730 A101637 A011729 this_sequence A133010 A071031 A011727
%K A011728 nonn
%O A011728 0,1
%A A011728 njas

%I A133010
%S A133010 0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,1,0,0,1,0,0,
%T A133010 0,0,1,0,0,1,0,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0,0,0,1,0,1,0,0,1,
%U A133010 0,1,0,0,0,1,1,0
%N A133010 Characteristic function of the Riemann zeta function: If n is a nearest integer to imaginary part of zero, then a(n)=1 else a(n)=0.
%C A133010 Also an insteresting triangle read by row: See tabl.
%e A133010 a(30)=1 because 30 is the nearest integer to imaginary part of 4th nontrivial zero of Riemann zeta function.
%Y A133010 See A002410 for more information. Cf. A058303, A065434, A065452, A065453.
%Y A133010 Adjacent sequences: A133007 A133008 A133009 this_sequence A133011 A133012 A133013
%Y A133010 Sequence in context: A101637 A011729 A011728 this_sequence A071031 A011727 A088918
%K A133010 easy,nonn,tabl
%O A133010 1,1
%A A133010 Omar E. Pol (info(AT)polprimos.com), Sep 13 2007

%I A071031
%S A071031 0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T A071031 0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
%U A071031 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0
%N A071031 Triangle read by rows giving successive states of cellular automaton generated by "rule 62".
%C A071031 Row n has length 2n+1.
%D A071031 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; Chapter 3.
%H A071031 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ce.html#cell">Index entries for sequences related to cellular automata</a>
%Y A071031 Adjacent sequences: A071028 A071029 A071030 this_sequence A071032 A071033 A071034
%Y A071031 Sequence in context: A011729 A011728 A133010 this_sequence A011727 A088918 A011726
%K A071031 nonn,tabf
%O A071031 0,1
%A A071031 Hans Havermann (pxp(AT)rogers.com), May 26 2002

%I A011727
%S A011727 0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,
%T A011727 1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,1,1,1,1,0,1,1,0,1,0,
%U A011727 1,1,1,1,0,0,0,1,0,0,0,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0,0
%N A011727 A binary m-sequence: expansion of reciprocal of x^14+x^12+x^11+x+1.
%D A011727 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011727 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011727 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011727 Adjacent sequences: A011724 A011725 A011726 this_sequence A011728 A011729 A011730
%Y A011727 Sequence in context: A011728 A133010 A071031 this_sequence A088918 A011726 A070109
%K A011727 nonn
%O A011727 0,1
%A A011727 njas

%I A088918
%S A088918 0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,
%T A088918 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
%U A088918 0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A088918 Number of representations of n as sum of two squares of distinct primes.
%C A088918 a(n) <= A000161(n); a(A088909(n)) > 0;
%C A088918 a(A088919(n)) = n and a(k) <> n for k<A088919(n).
%H A088918 <a href="http://www.research.att.com/~njas/sequences/Sindx_Su.html#ssq">Index entries for sequences related to sums of squares</a>
%e A088918 a(410)=2, see A088919.
%Y A088918 Cf. A002654.
%Y A088918 Adjacent sequences: A088915 A088916 A088917 this_sequence A088919 A088920 A088921
%Y A088918 Sequence in context: A133010 A071031 A011727 this_sequence A011726 A070109 A070207
%K A088918 nonn
%O A088918 1,1
%A A088918 Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Oct 23 2003

%I A011726
%S A011726 0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,
%T A011726 1,0,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,
%U A011726 1,0,1,0,0,1,1,0,0,0,1,1,0,0,0,0,0,0,1,0,0,1,0,1,1,0,1
%N A011726 A binary m-sequence: expansion of reciprocal of x^13+x^4+x^3+x+1.
%D A011726 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011726 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011726 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011726 Adjacent sequences: A011723 A011724 A011725 this_sequence A011727 A011728 A011729
%Y A011726 Sequence in context: A071031 A011727 A088918 this_sequence A070109 A070207 A107846
%K A011726 nonn
%O A011726 0,1
%A A011726 njas

%I A070109
%S A070109 0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,
%T A070109 0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,
%U A070109 0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A070109 Number of right integer triangles with perimeter n and relatively prime side lengths.
%C A070109 a(n)<=A024155(n); a(n)=A051493(n)-A070094(n)-A070102(n);
%C A070109 right integer triangles have integer areas: see A070142, A051516.
%C A070109 a(n) is nonzero iff n is in A024364.
%H A070109 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RightTriangle.html">Right Triangle</a>.
%H A070109 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PythagoreanTriple.html">Pythagorean Triples</a>.
%H A070109 R. Zumkeller, <a href="http://www.research.att.com/~njas/sequences/a070080.txt">Integer-sided triangles</a>
%F A070109 a(n)=A078926(n/2) if n is even; a(n)=0 if n is odd.
%e A070109 For n=30 there are A005044(30) = 19 integer triangles; only one is right: 5+12+13=30, 5^2+12^2 = 13^2; therefore a(30) = 1.
%Y A070109 Cf. A070080, A070081, A070082, A051493, A070093, A070101, A070138, A070084, A070137.
%Y A070109 Adjacent sequences: A070106 A070107 A070108 this_sequence A070110 A070111 A070112
%Y A070109 Sequence in context: A011727 A088918 A011726 this_sequence A070207 A107846 A065202
%K A070109 nonn
%O A070109 1,1
%A A070109 Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), May 05 2002

%I A070207
%S A070207 0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0
%N A070207 Duplicate of A024155.
%Y A070207 Adjacent sequences: A070204 A070205 A070206 this_sequence A070208 A070209 A070210
%Y A070207 Sequence in context: A088918 A011726 A070109 this_sequence A107846 A065202 A045701
%K A070207 dead
%O A070207 1,1

%I A107846
%S A107846 0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,
%T A107846 0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,
%U A107846 0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0
%N A107846 Number of duplicate digits of n.
%F A107846 a(n) = A055642(n) - A043537(n).
%e A107846 a(11) = 1 because 11 has two total decimal digits but only one distinct digit (1) and 2-1=1.
%e A107846 Similarly, a(3653135) = 7 (total digits) - 4 (distinct digits: 1,3,5,6) = 3 (There are three duplicate digits here, namely, 3, 3 and 5).
%Y A107846 Cf. A055642 (Total decimal digits of n), A043537 (Distinct decimal digits of n).
%Y A107846 Adjacent sequences: A107843 A107844 A107845 this_sequence A107847 A107848 A107849
%Y A107846 Sequence in context: A011726 A070109 A070207 this_sequence A065202 A045701 A011725
%K A107846 base,easy,nonn
%O A107846 0,1
%A A107846 Rick L. Shepherd (rshepherd2(AT)hotmail.com), May 24, 2005

%I A065202
%S A065202 0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,
%T A065202 1,0,0,0,1,0,0,0,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,1,0,0,0,0,1,0,0,
%U A065202 0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0,0,1,0
%N A065202 Characteristic function of A065201: a(n) = if A065201(k) = n for some k then 1 else 0.
%C A065202 a(A065200(n)) = 0 and a(A065201(n)) = 1.
%Y A065202 Cf. A065201, A065200.
%Y A065202 Adjacent sequences: A065199 A065200 A065201 this_sequence A065203 A065204 A065205
%Y A065202 Sequence in context: A070109 A070207 A107846 this_sequence A045701 A011725 A037808
%K A065202 nonn
%O A065202 1,1
%A A065202 Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Oct 21 2001
%E A065202 Edited by Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Oct 27 2006

%I A045701
%S A045701 0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,
%T A045701 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U A045701 0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A045701 Number of ways n can be written a sum of a square of a prime and a cube of a prime.
%e A045701 a(12) = 1 because 12=2^2+2^3; a(17) = 1 because 17=2^3+3^2.
%Y A045701 Adjacent sequences: A045698 A045699 A045700 this_sequence A045702 A045703 A045704
%Y A045701 Sequence in context: A070207 A107846 A065202 this_sequence A011725 A037808 A023973
%K A045701 easy,nonn
%O A045701 1,1
%A A045701 Felice Russo (felice.russo(AT)katamail.com)
%E A045701 More terms from Erich Friedman (erich.friedman(AT)stetson.edu).

%I A011725
%S A011725 0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,0,1,1,1,1,1,1,1,1,1,0,
%T A011725 0,1,1,0,1,0,0,0,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0,1,1,1,0,
%U A011725 0,1,0,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,1,0,1,1
%N A011725 A binary m-sequence: expansion of reciprocal of x^12+x^7+x^4+x^3+1.
%D A011725 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011725 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011725 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011725 Adjacent sequences: A011722 A011723 A011724 this_sequence A011726 A011727 A011728
%Y A011725 Sequence in context: A107846 A065202 A045701 this_sequence A037808 A023973 A044941
%K A011725 nonn
%O A011725 0,1
%A A011725 njas

%I A037808
%S A037808 0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,1,0,
%T A037808 0,0,0,1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,
%U A037808 0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,1,0
%N A037808 Number of i such that d(i)>d(i-1), where Sum{d(i)*10^i: i=0,1,...,m} is base 10 representation of n.
%Y A037808 Adjacent sequences: A037805 A037806 A037807 this_sequence A037809 A037810 A037811
%Y A037808 Sequence in context: A065202 A045701 A011725 this_sequence A023973 A044941 A011724
%K A037808 nonn,base
%O A037808 1,1
%A A037808 Clark Kimberling (ck6(AT)evansville.edu)

%I A023973
%S A023973 0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%T A023973 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,
%U A023973 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A023973 First bit in fractional part of binary expansion of 6-th root of n.
%t A023973 Array[ Function[ n, RealDigits[ N[ Power[ n, 1/6 ], 10 ], 2 ]// (#[ [ 1, #[ [ 2 ] ]+1 ] ])& ], 110 ]
%Y A023973 Adjacent sequences: A023970 A023971 A023972 this_sequence A023974 A023975 A023976
%Y A023973 Sequence in context: A045701 A011725 A037808 this_sequence A044941 A011724 A037807
%K A023973 nonn,base
%O A023973 1,1
%A A023973 njas, Olivier Gerard (ogerard(AT)ext.jussieu.fr)

%I A044941
%S A044941 0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,
%T A044941 0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,
%U A044941 0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0
%N A044941 Number of runs of even length in base 10 representation of n.
%C A044941 Period 11: (0,0,0,0,0,0,0,0,0,0,1) - Paolo P. Lava (ppl(AT)spl.at), Nov 29 2006
%F A044941 a(n)=1-[(n+1)^10 mod 11] with n>=0 - Paolo P. Lava (ppl(AT)spl.at), Nov 29 2006
%Y A044941 Adjacent sequences: A044938 A044939 A044940 this_sequence A044942 A044943 A044944
%Y A044941 Sequence in context: A011725 A037808 A023973 this_sequence A011724 A037807 A037817
%K A044941 nonn,base
%O A044941 1,1
%A A044941 Clark Kimberling (ck6(AT)evansville.edu)

%I A011724
%S A011724 0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,1,
%T A011724 0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,1,
%U A011724 0,0,1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0,1,1,1,1,1,1,0,0,0
%N A011724 A binary m-sequence: expansion of reciprocal of x^11+x^2+1.
%D A011724 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011724 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011724 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011724 Adjacent sequences: A011721 A011722 A011723 this_sequence A011725 A011726 A011727
%Y A011724 Sequence in context: A037808 A023973 A044941 this_sequence A037807 A037817 A025468
%K A011724 nonn
%O A011724 0,1
%A A011724 njas

%I A037807
%S A037807 0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,
%T A037807 1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,
%U A037807 1,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,0
%N A037807 Number of i such that d(i)>d(i-1), where Sum{d(i)*9^i: i=0,1,...,m} is base 9 representation of n.
%Y A037807 Adjacent sequences: A037804 A037805 A037806 this_sequence A037808 A037809 A037810
%Y A037807 Sequence in context: A023973 A044941 A011724 this_sequence A037817 A025468 A025465
%K A037807 nonn,base
%O A037807 1,1
%A A037807 Clark Kimberling (ck6(AT)evansville.edu)

%I A037817
%S A037817 0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,0,0,1,1,1,1,1,1,1,1,0,
%T A037817 0,0,1,1,1,1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,
%U A037817 0,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,1,1,0
%N A037817 Number of i such that d(i)>=d(i-1), where Sum{d(i)*10^i: i=0,1,...,m} is base 10 representation of n.
%Y A037817 Adjacent sequences: A037814 A037815 A037816 this_sequence A037818 A037819 A037820
%Y A037817 Sequence in context: A044941 A011724 A037807 this_sequence A025468 A025465 A044940
%K A037817 nonn,base
%O A037817 1,1
%A A037817 Clark Kimberling (ck6(AT)evansville.edu)

%I A025468
%S A025468 0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,
%T A025468 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
%U A025468 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A025468 Number of partitions of n into 2 distinct positive cubes.
%Y A025468 Adjacent sequences: A025465 A025466 A025467 this_sequence A025469 A025470 A025471
%Y A025468 Sequence in context: A011724 A037807 A037817 this_sequence A025465 A044940 A037825
%K A025468 nonn
%O A025468 0,1
%A A025468 David W. Wilson (davidwwilson(AT)comcast.net)

%I A025465
%S A025465 0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,
%T A025465 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
%U A025465 1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0
%N A025465 Number of partitions of n into 3 distinct nonnegative cubes.
%Y A025465 Adjacent sequences: A025462 A025463 A025464 this_sequence A025466 A025467 A025468
%Y A025465 Sequence in context: A037807 A037817 A025468 this_sequence A044940 A037825 A011723
%K A025465 nonn
%O A025465 0,1
%A A025465 David W. Wilson (davidwwilson(AT)comcast.net)

%I A044940
%S A044940 0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,
%T A044940 0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,
%U A044940 0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,1
%N A044940 Number of runs of even length in base 9 representation of n.
%Y A044940 Adjacent sequences: A044937 A044938 A044939 this_sequence A044941 A044942 A044943
%Y A044940 Sequence in context: A037817 A025468 A025465 this_sequence A037825 A011723 A037913
%K A044940 nonn,base
%O A044940 1,1
%A A044940 Clark Kimberling (ck6(AT)evansville.edu)

%I A037825
%S A037825 0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,1,
%T A037825 1,1,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,
%U A037825 1,1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,1,1,0,0,1
%N A037825 Number of i such that d(i)<d(i-1), where Sum{d(i)*10^i: i=0,1,....,m} is base 10 representation of n.
%Y A037825 Adjacent sequences: A037822 A037823 A037824 this_sequence A037826 A037827 A037828
%Y A037825 Sequence in context: A025468 A025465 A044940 this_sequence A011723 A037913 A037833
%K A037825 nonn,base
%O A037825 1,1
%A A037825 Clark Kimberling (ck6(AT)evansville.edu)

%I A011723
%S A011723 0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,1,1,0,
%T A011723 1,0,1,1,1,1,1,0,0,1,1,0,0,0,1,1,1,1,1,0,0,1,0,0,0,1,1,
%U A011723 1,0,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1
%N A011723 A binary m-sequence: expansion of reciprocal of x^10+x^3+1.
%D A011723 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011723 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011723 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011723 Adjacent sequences: A011720 A011721 A011722 this_sequence A011724 A011725 A011726
%Y A011723 Sequence in context: A025465 A044940 A037825 this_sequence A037913 A037833 A037816
%K A011723 nonn
%O A011723 0,1
%A A011723 njas

%I A037913
%S A037913 0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,
%T A037913 0,1,0,1,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,
%U A037913 0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,1,0
%N A037913 Number of i such that |d(i)-d(i-1)| = 1, where Sum{d(i)*10^i: i=0,1,...,m} is base 10 representation of n.
%Y A037913 Adjacent sequences: A037910 A037911 A037912 this_sequence A037914 A037915 A037916
%Y A037913 Sequence in context: A044940 A037825 A011723 this_sequence A037833 A037816 A071032
%K A037913 nonn,base
%O A037913 1,1
%A A037913 Clark Kimberling (ck6(AT)evansville.edu)

%I A037833
%S A037833 0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,1,
%T A037833 1,1,1,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,1,
%U A037833 1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,1,1,0,0,1,1,1,1,1,1,1,1,1,0,1
%N A037833 Number of i such that d(i)<=d(i-1), where Sum{d(i)*10^i: i=0,1,...,m} is base 10 representation of n.
%Y A037833 Adjacent sequences: A037830 A037831 A037832 this_sequence A037834 A037835 A037836
%Y A037833 Sequence in context: A037825 A011723 A037913 this_sequence A037816 A071032 A044939
%K A037833 nonn,base
%O A037833 1,1
%A A037833 Clark Kimberling (ck6(AT)evansville.edu)

%I A037816
%S A037816 0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,1,
%T A037816 1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0,1,
%U A037816 1,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1
%N A037816 Number of i such that d(i)>=d(i-1), where Sum{d(i)*9^i: i=0,1,...,m} is base 9 representation of n.
%Y A037816 Adjacent sequences: A037813 A037814 A037815 this_sequence A037817 A037818 A037819
%Y A037816 Sequence in context: A011723 A037913 A037833 this_sequence A071032 A044939 A037824
%K A037816 nonn,base
%O A037816 1,1
%A A037816 Clark Kimberling (ck6(AT)evansville.edu)

%I A071032
%S A071032 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,
%T A071032 0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,
%U A071032 0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,1,1,1,1,0,1,1,1,1,0,0,0,1,0,0
%N A071032 Triangle read by rows giving successive states of cellular automaton generated by "rule 86".
%C A071032 Row n has length 2n+1.
%D A071032 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; Chapter 3.
%H A071032 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ce.html#cell">Index entries for sequences related to cellular automata</a>
%Y A071032 Adjacent sequences: A071029 A071030 A071031 this_sequence A071033 A071034 A071035
%Y A071032 Sequence in context: A037913 A037833 A037816 this_sequence A044939 A037824 A025461
%K A071032 nonn,tabf
%O A071032 0,1
%A A071032 Hans Havermann (pxp(AT)rogers.com), May 26 2002

%I A044939
%S A044939 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,
%T A044939 0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
%U A044939 0,0,1,1,0,0,0,0,0,0,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0
%N A044939 Number of runs of even length in base 8 representation of n.
%Y A044939 Adjacent sequences: A044936 A044937 A044938 this_sequence A044940 A044941 A044942
%Y A044939 Sequence in context: A037833 A037816 A071032 this_sequence A037824 A025461 A045698
%K A044939 nonn,base
%O A044939 1,1
%A A044939 Clark Kimberling (ck6(AT)evansville.edu)

%I A037824
%S A037824 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,1,1,1,0,
%T A037824 0,0,0,0,0,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,
%U A037824 0,0,1,1,1,1,1,1,1,0,0,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1
%N A037824 Number of i such that d(i)<d(i-1), where Sum{d(i)*9^i: i=0,1,....,m} is base 9 representation of n.
%Y A037824 Adjacent sequences: A037821 A037822 A037823 this_sequence A037825 A037826 A037827
%Y A037824 Sequence in context: A037816 A071032 A044939 this_sequence A025461 A045698 A011722
%K A037824 nonn,base
%O A037824 1,1
%A A037824 Clark Kimberling (ck6(AT)evansville.edu)

%I A025461
%S A025461 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,0,
%T A025461 1,0,0,0,0,1,0,1,0,0,0,0,1,0,1,0,0,0,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,1,
%U A025461 0,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1
%N A025461 Number of partitions of n into 8 positive cubes.
%Y A025461 Adjacent sequences: A025458 A025459 A025460 this_sequence A025462 A025463 A025464
%Y A025461 Sequence in context: A071032 A044939 A037824 this_sequence A045698 A011722 A044938
%K A025461 nonn
%O A025461 0,1
%A A025461 David W. Wilson (davidwwilson(AT)comcast.net)

%I A045698
%S A045698 0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,
%T A045698 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,
%U A045698 0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0
%N A045698 Number of ways n can be written as sum of two prime squares.
%H A045698 <a href="http://www.research.att.com/~njas/sequences/Sindx_Su.html#ssq">Index entries for sequences related to sums of squares</a>
%F A045698 For example a(29) = 1 because 29=2^2+5^2. a(3)=0 because there is no way to write 3 as sum of two squares of primes.
%Y A045698 Adjacent sequences: A045695 A045696 A045697 this_sequence A045699 A045700 A045701
%Y A045698 Sequence in context: A044939 A037824 A025461 this_sequence A011722 A044938 A072401
%K A045698 easy,nonn
%O A045698 0,1
%A A045698 Felice Russo (felice.russo(AT)katamail.com)
%E A045698 More terms from Erich Friedman (erich.friedman(AT)stetson.edu).

%I A011722
%S A011722 0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,1,1,0,0,1,0,0,0,1,1,1,
%T A011722 0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0,0,1,0,1,0,1,
%U A011722 0,0,0,1,1,0,1,1,0,0,1,1,1,1,1,0,0,1,1,1,1,0,0,0,1,0,1
%N A011722 A binary m-sequence: expansion of reciprocal of x^9+x^4+1.
%D A011722 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011722 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011722 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011722 Adjacent sequences: A011719 A011720 A011721 this_sequence A011723 A011724 A011725
%Y A011722 Sequence in context: A037824 A025461 A045698 this_sequence A044938 A072401 A064873
%K A011722 nonn
%O A011722 0,1
%A A011722 njas

%I A044938
%S A044938 0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
%T A044938 0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,1,0,1,1,1,
%U A044938 1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0
%N A044938 Number of runs of even length in base 7 representation of n.
%Y A044938 Adjacent sequences: A044935 A044936 A044937 this_sequence A044939 A044940 A044941
%Y A044938 Sequence in context: A025461 A045698 A011722 this_sequence A072401 A064873 A037823
%K A044938 nonn,base
%O A044938 1,1
%A A044938 Clark Kimberling (ck6(AT)evansville.edu)

%I A072401
%S A072401 0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,0,0,0,0,
%T A072401 0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,
%U A072401 1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,0
%N A072401 1 iff n is of the form 4^m*(8k+7).
%C A072401 Characteristic function of A004215, indicating numbers not the sum of 3 integer squares.
%D A072401 J.-P. Allouche and J. Shallit, The ring of k-regular sequences (Example 20), Theoretical Computer Science, 98 (1992), 163-197.
%H A072401 J.-P. Allouche and J. Shallit, <a href="http://www.cs.uwaterloo.ca/~shallit/Papers/as0.ps">The ring of k-regular sequences</a>, Theoretical Computer Sci., 98 (1992), 163-197.
%H A072401 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SquareNumber.html">Square Numbers.</a>
%H A072401 <a href="http://www.research.att.com/~njas/sequences/Sindx_Su.html#ssq">Index entries for sequences related to sums of squares.</a>
%F A072401 a(n) = 1 - A057427(7 - A072400(n)).
%Y A072401 a(A004215(k)) = 1 for k>0, a(n) = A057427(A064873(n)), for k<112: a(n)=A064873(n), but A064873(112)=2, as also a(112 - 1) = 1.
%Y A072401 Cf. A071374.
%Y A072401 Adjacent sequences: A072398 A072399 A072400 this_sequence A072402 A072403 A072404
%Y A072401 Sequence in context: A045698 A011722 A044938 this_sequence A064873 A037823 A115790
%K A072401 nonn
%O A072401 0,1
%A A072401 Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Jun 16 2002

%I A064873
%S A064873 0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,0,0,0,
%T A064873 0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,0,0,0,0,0,0,
%U A064873 0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,1,0
%N A064873 First of four sequences representing the lexicographical minimal decomposition of n in 4 squares: n = a(n)^2 + A064874(n)^2 + A064875(n)^2 + A064876(n)^2.
%C A064873 A072401(n) = A057427(a(n)).
%C A064873 For k<112: a(n)=A072401(n), but A072401(112) = 1<>a(112)=2, as also A072401(112 - 1) = 1.
%H A064873 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SquareNumber.html">Square Numbers.</a>
%H A064873 <a href="http://www.research.att.com/~njas/sequences/Sindx_Su.html#ssq">Index entries for sequences related to sums of squares.</a>
%e A064873 a(25) = 0: 25 = a(25)^2 + A064874(25)^2 + A064875(25)^2 + A064876(25)^2 = 0 + 0 + 0 + 25 and the other decompositions (0, 0, 3, 4) and (1, 2, 2, 4) are greater than (0, 0, 0, 5).
%Y A064873 Cf. A064874, A064875, A064876, A071374.
%Y A064873 Adjacent sequences: A064870 A064871 A064872 this_sequence A064874 A064875 A064876
%Y A064873 Sequence in context: A011722 A044938 A072401 this_sequence A037823 A115790 A025460
%K A064873 nonn
%O A064873 0,1
%A A064873 Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Oct 10 2001

%I A037823
%S A037823 0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0,
%T A037823 0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,1,1,1,1,1,
%U A037823 1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,1,1,1
%N A037823 Number of i such that d(i)<d(i-1), where Sum{d(i)*8^i: i=0,1,....,m} is base 8 representation of n.
%Y A037823 Adjacent sequences: A037820 A037821 A037822 this_sequence A037824 A037825 A037826
%Y A037823 Sequence in context: A044938 A072401 A064873 this_sequence A115790 A025460 A101605
%K A037823 nonn,base
%O A037823 1,1
%A A037823 Clark Kimberling (ck6(AT)evansville.edu)

%I A115790
%S A115790 0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,
%T A115790 1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,
%U A115790 1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0
%N A115790 1 - (Floor((n+1)*pi)-Floor(n*pi)) mod 2.
%C A115790 The arithmetic mean 1/(n+1)*sum(a(k)|k=0...n) converges to pi-3. What is effectively the same: the Cesaro limit (C1) of a(n) is pi-3.
%F A115790 a(n) = 1 - (Floor((n+1)*pi)-Floor(n*pi)) mod 2.
%e A115790 a(6)=0 because 7*pi=21.99, 6*pi=18.85 and so a(6)=1-(21-18) mod 2 = 0;
%e A115790 a(7)=1 because 8*pi=25.13 and so a(7)=1-(25-21) mod 2 = 1;
%Y A115790 Cf. A022844, A115787, A115788, A115789.
%Y A115790 Adjacent sequences: A115787 A115788 A115789 this_sequence A115791 A115792 A115793
%Y A115790 Sequence in context: A072401 A064873 A037823 this_sequence A025460 A101605 A135133
%K A115790 nonn
%O A115790 0,1
%A A115790 Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jan 31 2006

%I A025460
%S A025460 0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,0,1,
%T A025460 0,0,0,0,1,0,1,0,0,0,0,1,0,1,0,0,0,0,1,0,1,0,0,1,0,1,0,0,0,0,1,0,1,0,1,0,
%U A025460 0,1,0,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,1,0
%N A025460 Number of partitions of n into 7 positive cubes.
%Y A025460 Adjacent sequences: A025457 A025458 A025459 this_sequence A025461 A025462 A025463
%Y A025460 Sequence in context: A064873 A037823 A115790 this_sequence A101605 A135133 A011712
%K A025460 nonn
%O A025460 0,1
%A A025460 David W. Wilson (davidwwilson(AT)comcast.net)

%I A101605
%S A101605 0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,0,1,1,0,1,0,0,0,0,0,
%T A101605 0,0,0,0,0,0,1,0,1,1,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,0,1,
%U A101605 0,0,0,0,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,1,0
%N A101605 a(n) = 1 iff n is a product of exactly 3 primes, otherwise 0.
%C A101605 "3-almost prime numbers" are a generalization of primes and semiprimes. As explained in Weisstein: "The primes correspond to the "1-almost prime" numbers 2, 3, 5, 7, 11, ... (A000040). The 2-almost prime numbers correspond to semiprimes 4, 6, 9, 10, 14, 15, 21, 22, ... (A001358). The first few 3-almost primes are 8, 12, 18, 20, 27, 28, 30, 42, 44, 45, 50, 52, 63, 66, 68, 70, 75, 76, 78, 92, 98, 99, ... (A014612). The first few 4-almost primes are 16, 24, 36, 40, 54, 56, 60, 81, 84, 88, 90, 100, ... (A014613). The first few 5-almost primes are 32, 48, 72, 80, ... (A014614)." See A101606 for the Inverse Moebius Transform of this sequence.
%H A101605 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AlmostPrime.html">Almost Prime</a>.
%F A101605 a(n) = 1 iff n has exactly three prime factors (not necessarily distinct), else a(n) = 0. a(n) = 1 iff n is an element of A014612, else a(n) = 0.
%e A101605 a(28) = 1 because 28 = 2 * 2 * 7 is the product of exactly 3 primes, counted with multiplicity.
%Y A101605 Cf. A014612, A101606, A001358, A014613, A014614.
%Y A101605 Adjacent sequences: A101602 A101603 A101604 this_sequence A101606 A101607 A101608
%Y A101605 Sequence in context: A037823 A115790 A025460 this_sequence A135133 A011712 A011715
%K A101605 easy,nonn
%O A101605 0,1
%A A101605 Jonathan Vos Post (jvospost2(AT)yahoo.com), Dec 09 2004

%I A135133
%S A135133 0,0,0,0,0,0,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,1,1,1,1,1,1,0,0,0,
%T A135133 1,0,1,1,1,0,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0
%N A135133 a(n) = (floor function(S2(n)/3)) mod 2, where S2(n) denotes the binary weight of n.
%C A135133 A generalized Thue-Morse sequence.
%D A135133 Ricardo Astudillo, On a class of Thue-Morse type sequences, Journal of Integer Sequences, Vol. 6 (2003),article 04.3.2
%Y A135133 Cf. A010060.
%Y A135133 Adjacent sequences: A135130 A135131 A135132 this_sequence A135134 A135135 A135136
%Y A135133 Sequence in context: A115790 A025460 A101605 this_sequence A011712 A011715 A011721
%K A135133 nonn
%O A135133 0,1
%A A135133 Ctibor O. Zizka (ctibor.zizka(AT)seznam.cz), Feb 12 2008

%I A011712
%S A011712 0,0,0,0,0,0,0,1,0,0,0,1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,1,
%T A011712 1,1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,1,1,1,0,0,0,
%U A011712 0,0,0,0,1,0,0,0,1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,1,1,1,1
%N A011712 A binary m-sequence: expansion of reciprocal of x^8+x^7+x^5+x^4+1.
%D A011712 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011712 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011712 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011712 Adjacent sequences: A011709 A011710 A011711 this_sequence A011713 A011714 A011715
%Y A011712 Sequence in context: A025460 A101605 A135133 this_sequence A011715 A011721 A011694
%K A011712 nonn
%O A011712 0,1
%A A011712 njas

%I A011715
%S A011715 0,0,0,0,0,0,0,1,0,0,0,1,1,1,0,0,0,1,0,0,1,0,1,1,1,0,0,
%T A011715 0,0,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0,0,
%U A011715 0,1,0,1,0,1,1,0,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,1,1
%N A011715 A binary m-sequence: expansion of reciprocal of x^8+x^6+x^5+x^4+1.
%D A011715 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011715 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011715 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011715 Adjacent sequences: A011712 A011713 A011714 this_sequence A011716 A011717 A011718
%Y A011715 Sequence in context: A101605 A135133 A011712 this_sequence A011721 A011694 A011696
%K A011715 nonn
%O A011715 0,1
%A A011715 njas

%I A011721
%S A011721 0,0,0,0,0,0,0,1,0,0,1,0,1,0,0,1,1,1,1,1,1,1,1,0,0,0,1,
%T A011721 1,0,0,0,1,0,1,0,1,0,1,0,0,0,0,1,0,0,0,0,1,1,0,0,1,1,0,
%U A011721 0,0,0,0,1,1,1,1,1,0,1,1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,1
%N A011721 A binary m-sequence: expansion of reciprocal of x^8+x^6+x^5+x^3+1.
%D A011721 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011721 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011721 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011721 Adjacent sequences: A011718 A011719 A011720 this_sequence A011722 A011723 A011724
%Y A011721 Sequence in context: A135133 A011712 A011715 this_sequence A011694 A011696 A011693
%K A011721 nonn
%O A011721 0,1
%A A011721 njas

%I A011694
%S A011694 0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,1,1,1,0,0,0,1,1,0,1,
%T A011694 0,1,0,1,0,1,1,1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,0,
%U A011694 1,0,0,0,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0,1,0,0
%N A011694 A binary m-sequence: expansion of reciprocal of x^8+x^7+x^5+x^3+1.
%D A011694 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011694 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011694 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011694 Adjacent sequences: A011691 A011692 A011693 this_sequence A011695 A011696 A011697
%Y A011694 Sequence in context: A011712 A011715 A011721 this_sequence A011696 A011693 A011695
%K A011694 nonn
%O A011694 0,1
%A A011694 njas

%I A011696
%S A011696 0,0,0,0,0,0,0,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0,1,1,
%T A011696 1,0,0,1,1,1,0,0,0,1,1,1,1,1,1,0,1,0,1,1,0,0,0,1,1,0,1,
%U A011696 1,0,1,0,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,1,1,1,0,0
%N A011696 A binary m-sequence: expansion of reciprocal of x^8+x^7+x^6+x^5+x^4+x^3+1.
%D A011696 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011696 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011696 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011696 Adjacent sequences: A011693 A011694 A011695 this_sequence A011697 A011698 A011699
%Y A011696 Sequence in context: A011715 A011721 A011694 this_sequence A011693 A011695 A011706
%K A011696 nonn
%O A011696 0,1
%A A011696 njas

%I A011693
%S A011693 0,0,0,0,0,0,0,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,
%T A011693 1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,1,0,0,1,0,0,0,
%U A011693 0,0,0,0,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1
%N A011693 A binary m-sequence: expansion of reciprocal of x^8+x^5+x^4+x^3+1.
%D A011693 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011693 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011693 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011693 Adjacent sequences: A011690 A011691 A011692 this_sequence A011694 A011695 A011696
%Y A011693 Sequence in context: A011721 A011694 A011696 this_sequence A011695 A011706 A011697
%K A011693 nonn
%O A011693 0,1
%A A011693 njas

%I A011695
%S A011695 0,0,0,0,0,0,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0,1,0,1,1,1,
%T A011695 0,1,1,1,0,1,0,1,1,1,0,0,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0,
%U A011695 1,1,0,0,0,1,1,1,1,1,1,0,1,1,0,1,0,1,1,0,0,1,1,0,1,1,0
%N A011695 A binary m-sequence: expansion of reciprocal of x^8+x^7+x^6+x^5+x^4+x^2+1.
%D A011695 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011695 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011695 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011695 Adjacent sequences: A011692 A011693 A011694 this_sequence A011696 A011697 A011698
%Y A011695 Sequence in context: A011694 A011696 A011693 this_sequence A011706 A011697 A011703
%K A011695 nonn
%O A011695 0,1
%A A011695 njas

%I A011706
%S A011706 0,0,0,0,0,0,0,1,0,1,0,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,0,
%T A011706 0,0,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,0,0,0,0,1,0,0,
%U A011706 0,0,1,1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0,1,0,0
%N A011706 A binary m-sequence: expansion of reciprocal of x^8+x^6+x^5+x^2+1.
%D A011706 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011706 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011706 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011706 Adjacent sequences: A011703 A011704 A011705 this_sequence A011707 A011708 A011709
%Y A011706 Sequence in context: A011696 A011693 A011695 this_sequence A011697 A011703 A011702
%K A011706 nonn
%O A011706 0,1
%A A011706 njas

%I A011697
%S A011697 0,0,0,0,0,0,0,1,0,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,1,1,1,
%T A011697 1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0,0,1,1,1,1,1,0,1,0,1,0,
%U A011697 1,0,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0,1,0,1,1,0,0,1,1,0,0
%N A011697 A binary m-sequence: expansion of reciprocal of x^8+x^4+x^3+x^2+1.
%D A011697 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011697 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011697 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011697 Adjacent sequences: A011694 A011695 A011696 this_sequence A011698 A011699 A011700
%Y A011697 Sequence in context: A011693 A011695 A011706 this_sequence A011703 A011702 A011705
%K A011697 nonn
%O A011697 0,1
%A A011697 njas

%I A011703
%S A011703 0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,1,1,0,1,1,1,0,1,0,0,1,0,
%T A011703 1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0,1,0,1,0,0,1,0,0,1,0,
%U A011703 0,0,0,1,1,0,1,0,0,0,1,0,1,0,1,1,1,1,1,0,1,0,1,0,1,1,0
%N A011703 A binary m-sequence: expansion of reciprocal of x^8+x^7+x^6+x^4+x^3+x^2+1.
%D A011703 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011703 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011703 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011703 Adjacent sequences: A011700 A011701 A011702 this_sequence A011704 A011705 A011706
%Y A011703 Sequence in context: A011695 A011706 A011697 this_sequence A011702 A011705 A011704
%K A011703 nonn
%O A011703 0,1
%A A011703 njas

%I A011702
%S A011702 0,0,0,0,0,0,0,1,0,1,1,0,1,0,0,1,0,0,0,0,0,0,1,1,1,0,1,
%T A011702 1,1,0,1,1,0,0,0,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0,0,0,1,1,
%U A011702 0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,1,1,1,1,1,1,1,0,0,1,0
%N A011702 A binary m-sequence: expansion of reciprocal of x^8+x^7+x^5+x^4+x^3+x^2+1.
%D A011702 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011702 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011702 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011702 Adjacent sequences: A011699 A011700 A011701 this_sequence A011703 A011704 A011705
%Y A011702 Sequence in context: A011706 A011697 A011703 this_sequence A011705 A011704 A011717
%K A011702 nonn
%O A011702 0,1
%A A011702 njas

%I A011705
%S A011705 0,0,0,0,0,0,0,1,0,1,1,1,0,0,0,1,1,1,0,1,1,1,1,0,0,0,1,
%T A011705 0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,1,1,0,0,1,1,1,0,0,0,0,
%U A011705 1,0,1,0,1,1,1,1,1,1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,1,0,1
%N A011705 A binary m-sequence: expansion of reciprocal of x^8+x^7+x^3+x^2+1.
%D A011705 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011705 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011705 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011705 Adjacent sequences: A011702 A011703 A011704 this_sequence A011706 A011707 A011708
%Y A011705 Sequence in context: A011697 A011703 A011702 this_sequence A011704 A011717 A103675
%K A011705 nonn
%O A011705 0,1
%A A011705 njas

%I A011704
%S A011704 0,0,0,0,0,0,0,1,0,1,1,1,0,1,1,1,1,0,1,1,0,0,1,1,1,1,1,
%T A011704 1,1,1,0,0,1,0,1,1,0,1,0,1,1,0,1,1,1,0,1,0,1,0,1,0,1,1,
%U A011704 1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0,0,1
%N A011704 A binary m-sequence: expansion of reciprocal of x^8+x^6+x^3+x^2+1.
%D A011704 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011704 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011704 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011704 Adjacent sequences: A011701 A011702 A011703 this_sequence A011705 A011706 A011707
%Y A011704 Sequence in context: A011703 A011702 A011705 this_sequence A011717 A103675 A011701
%K A011704 nonn
%O A011704 0,1
%A A011704 njas

%I A011717
%S A011717 0,0,0,0,0,0,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,1,0,0,
%T A011717 0,1,1,0,1,0,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,0,0,0,0,1,1,
%U A011717 0,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,1,1,0
%N A011717 A binary m-sequence: expansion of reciprocal of x^8+x^5+x^3+x^2+1.
%D A011717 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011717 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011717 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011717 Adjacent sequences: A011714 A011715 A011716 this_sequence A011718 A011719 A011720
%Y A011717 Sequence in context: A011702 A011705 A011704 this_sequence A103675 A011701 A011692
%K A011717 nonn
%O A011717 0,1
%A A011717 njas

%I A103675
%S A103675 0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T A103675 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U A103675 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0
%N A103675 If in binary representation n! contains 7! then 1 else 0.
%C A103675 a(A103680(n)) = 1, a(A103681(n)) = 0.
%H A103675 <a href="http://www.research.att.com/~njas/sequences/Sindx_Fa.html#factorial">Index entries for sequences related to factorial numbers</a>
%H A103675 <a href="http://www.research.att.com/~njas/sequences/Sindx_Bi.html#binary">Index entries for sequences related to binary expansion of n</a>
%Y A103675 Cf. A102730, A036603, A007088, A000142, A103673, A103674.
%Y A103675 Adjacent sequences: A103672 A103673 A103674 this_sequence A103676 A103677 A103678
%Y A103675 Sequence in context: A011705 A011704 A011717 this_sequence A011701 A011692 A011720
%K A103675 nonn
%O A103675 0,1
%A A103675 Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Feb 12 2005

%I A011701
%S A011701 0,0,0,0,0,0,0,1,1,0,0,0,0,1,1,1,0,1,0,1,1,0,0,1,1,0,0,
%T A011701 1,0,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,1,1,1,1,
%U A011701 1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0,1,1
%N A011701 A binary m-sequence: expansion of reciprocal of x^8+x^5+x^4+x^3+x^2+x+1.
%D A011701 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011701 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011701 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011701 Adjacent sequences: A011698 A011699 A011700 this_sequence A011702 A011703 A011704
%Y A011701 Sequence in context: A011704 A011717 A103675 this_sequence A011692 A011720 A011708
%K A011701 nonn
%O A011701 0,1
%A A011701 njas

%I A011692
%S A011692 0,0,0,0,0,0,0,1,1,0,0,0,1,0,0,0,0,0,1,1,1,1,0,1,0,1,0,
%T A011692 0,0,1,1,0,0,1,0,0,0,0,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,
%U A011692 0,0,1,0,0,1,1,0,1,1,0,1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0
%N A011692 A binary m-sequence: expansion of reciprocal of x^8+x^6+x^4+x^3+x^2+x+1.
%D A011692 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011692 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011692 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011692 Adjacent sequences: A011689 A011690 A011691 this_sequence A011693 A011694 A011695
%Y A011692 Sequence in context: A011717 A103675 A011701 this_sequence A011720 A011708 A011707
%K A011692 nonn
%O A011692 0,1
%A A011692 njas

%I A011720
%S A011720 0,0,0,0,0,0,0,1,1,0,0,0,1,1,1,1,1,0,1,0,0,1,0,1,1,0,1,
%T A011720 1,0,1,0,0,0,0,0,1,0,0,1,0,1,0,1,1,1,0,0,1,1,1,1,0,0,0,
%U A011720 0,0,0,0,1,1,0,0,0,1,1,1,1,1,0,1,0,0,1,0,1,1,0,1,1,0,1
%N A011720 A binary m-sequence: expansion of reciprocal of x^8+x^7+x^4+x^3+x^2+x+1.
%D A011720 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011720 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011720 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011720 Adjacent sequences: A011717 A011718 A011719 this_sequence A011721 A011722 A011723
%Y A011720 Sequence in context: A103675 A011701 A011692 this_sequence A011708 A011707 A011698
%K A011720 nonn
%O A011720 0,1
%A A011720 njas

%I A011708
%S A011708 0,0,0,0,0,0,0,1,1,0,0,1,1,1,1,1,0,1,0,0,0,1,1,0,1,1,0,
%T A011708 1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0,0,1,0,0,1,0,
%U A011708 0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,1,1,1,1,0,1
%N A011708 A binary m-sequence: expansion of reciprocal of x^8+x^7+x^6+x^3+x^2+x+1.
%D A011708 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011708 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011708 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011708 Adjacent sequences: A011705 A011706 A011707 this_sequence A011709 A011710 A011711
%Y A011708 Sequence in context: A011701 A011692 A011720 this_sequence A011707 A011698 A011709
%K A011708 nonn
%O A011708 0,1
%A A011708 njas

%I A011707
%S A011707 0,0,0,0,0,0,0,1,1,0,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,0,
%T A011707 1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0,1,0,1,1,0,0,0,
%U A011707 0,0,0,0,1,1,0,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0
%N A011707 A binary m-sequence: expansion of reciprocal of x^8+x^7+x^6+x^4+x^2+x+1.
%D A011707 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011707 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011707 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011707 Adjacent sequences: A011704 A011705 A011706 this_sequence A011708 A011709 A011710
%Y A011707 Sequence in context: A011692 A011720 A011708 this_sequence A011698 A011709 A011711
%K A011707 nonn
%O A011707 0,1
%A A011707 njas

%I A011698
%S A011698 0,0,0,0,0,0,0,1,1,0,1,0,1,1,0,1,0,1,0,1,1,1,1,1,0,1,0,
%T A011698 1,0,0,0,1,0,1,1,0,0,0,0,1,0,0,1,0,0,1,0,1,0,0,0,0,1,1,
%U A011698 0,0,1,1,0,0,0,1,1,1,1,0,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0
%N A011698 A binary m-sequence: expansion of reciprocal of x^8+x^6+x^5+x^4+x^2+x+1.
%D A011698 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011698 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011698 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011698 Adjacent sequences: A011695 A011696 A011697 this_sequence A011699 A011700 A011701
%Y A011698 Sequence in context: A011720 A011708 A011707 this_sequence A011709 A011711 A011714
%K A011698 nonn
%O A011698 0,1
%A A011698 njas

%I A011709
%S A011709 0,0,0,0,0,0,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0,1,1,1,
%T A011709 1,0,0,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0,1,1,0,0,0,1,1,1,0,
%U A011709 0,0,0,1,1,0,0,0,0,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,1,0
%N A011709 A binary m-sequence: expansion of reciprocal of x^8+x^7+x^2+x+1.
%D A011709 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011709 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011709 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011709 Adjacent sequences: A011706 A011707 A011708 this_sequence A011710 A011711 A011712
%Y A011709 Sequence in context: A011708 A011707 A011698 this_sequence A011711 A011714 A011718
%K A011709 nonn
%O A011709 0,1
%A A011709 njas

%I A011711
%S A011711 0,0,0,0,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,1,1,1,
%T A011711 0,0,0,0,0,1,1,1,0,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0,0,1,1,
%U A011711 0,0,0,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,1,1,1,1
%N A011711 A binary m-sequence: expansion of reciprocal of x^8+x^7+x^6+x^5+x^2+x+1.
%D A011711 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011711 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011711 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011711 Adjacent sequences: A011708 A011709 A011710 this_sequence A011712 A011713 A011714
%Y A011711 Sequence in context: A011707 A011698 A011709 this_sequence A011714 A011718 A011700
%K A011711 nonn
%O A011711 0,1
%A A011711 njas

%I A011714
%S A011714 0,0,0,0,0,0,0,1,1,1,0,0,0,1,1,0,0,1,0,0,1,1,0,1,1,1,0,
%T A011714 0,1,1,1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0,0,0,
%U A011714 0,0,0,0,1,1,1,0,0,0,1,1,0,0,1,0,0,1,1,0,1,1,1,0,0,1,1
%N A011714 A binary m-sequence: expansion of reciprocal of x^8+x^4+x^3+x+1.
%D A011714 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011714 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011714 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011714 Adjacent sequences: A011711 A011712 A011713 this_sequence A011715 A011716 A011717
%Y A011714 Sequence in context: A011698 A011709 A011711 this_sequence A011718 A011700 A011719
%K A011714 nonn
%O A011714 0,1
%A A011714 njas

%I A011718
%S A011718 0,0,0,0,0,0,0,1,1,1,0,0,1,0,0,1,1,1,1,1,1,1,1,0,1,0,0,
%T A011718 0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,1,0,0,1,1,0,0,
%U A011718 1,0,0,0,0,0,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0,1,0
%N A011718 A binary m-sequence: expansion of reciprocal of x^8+x^6+x^5+x^4+x^3+x+1.
%D A011718 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011718 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011718 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011718 Adjacent sequences: A011715 A011716 A011717 this_sequence A011719 A011720 A011721
%Y A011718 Sequence in context: A011709 A011711 A011714 this_sequence A011700 A011719 A011716
%K A011718 nonn
%O A011718 0,1
%A A011718 njas

%I A011700
%S A011700 0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0,1,1,0,0,0,
%T A011700 1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,1,0,1,1,1,0,1,1,0,0,1,1,
%U A011700 0,0,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,1,1,0,1
%N A011700 A binary m-sequence: expansion of reciprocal of x^8+x^7+x^3+x+1.
%D A011700 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011700 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011700 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011700 Adjacent sequences: A011697 A011698 A011699 this_sequence A011701 A011702 A011703
%Y A011700 Sequence in context: A011711 A011714 A011718 this_sequence A011719 A011716 A011713
%K A011700 nonn
%O A011700 0,1
%A A011700 njas

%I A011719
%S A011719 0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0,1,1,0,1,0,
%T A011719 0,0,0,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,1,0,0,
%U A011719 0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,1,1
%N A011719 A binary m-sequence: expansion of reciprocal of x^8+x^5+x^3+x+1.
%D A011719 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011719 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011719 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011719 Adjacent sequences: A011716 A011717 A011718 this_sequence A011720 A011721 A011722
%Y A011719 Sequence in context: A011714 A011718 A011700 this_sequence A011716 A011713 A011699
%K A011719 nonn
%O A011719 0,1
%A A011719 njas

%I A011716
%S A011716 0,0,0,0,0,0,0,1,1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0,
%T A011716 0,1,0,1,1,0,1,1,0,1,0,0,1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,
%U A011716 0,0,0,0,1,1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0,1,0
%N A011716 A binary m-sequence: expansion of reciprocal of x^8+x^7+x^6+x^5+x^4+x+1.
%D A011716 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011716 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011716 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011716 Adjacent sequences: A011713 A011714 A011715 this_sequence A011717 A011718 A011719
%Y A011716 Sequence in context: A011718 A011700 A011719 this_sequence A011713 A011699 A011710
%K A011716 nonn
%O A011716 0,1
%A A011716 njas

%I A011713
%S A011713 0,0,0,0,0,0,0,1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0,0,1,0,0,
%T A011713 0,1,0,1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0,0,1,
%U A011713 0,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,1,1,1,1,0
%N A011713 A binary m-sequence: expansion of reciprocal of x^8+x^6+x^5+x+1.
%D A011713 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011713 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011713 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011713 Adjacent sequences: A011710 A011711 A011712 this_sequence A011714 A011715 A011716
%Y A011713 Sequence in context: A011700 A011719 A011716 this_sequence A011699 A011710 A135500
%K A011713 nonn
%O A011713 0,1
%A A011713 njas

%I A011699
%S A011699 0,0,0,0,0,0,0,1,1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,1,1,1,1,
%T A011699 0,0,1,1,0,0,0,0,1,0,0,1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,
%U A011699 1,0,1,0,0,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0,0,0,0,0,1
%N A011699 A binary m-sequence: expansion of reciprocal of x^8+x^7+x^5+x+1.
%D A011699 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011699 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011699 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011699 Adjacent sequences: A011696 A011697 A011698 this_sequence A011700 A011701 A011702
%Y A011699 Sequence in context: A011719 A011716 A011713 this_sequence A011710 A135500 A023972
%K A011699 nonn
%O A011699 0,1
%A A011699 njas

%I A011710
%S A011710 0,0,0,0,0,0,0,1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,1,0,
%T A011710 1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0,0,1,0,1,0,0,0,1,0,
%U A011710 0,1,0,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0
%N A011710 A binary m-sequence: expansion of reciprocal of x^8+x^7+x^6+x+1.
%D A011710 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011710 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011710 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011710 Adjacent sequences: A011707 A011708 A011709 this_sequence A011711 A011712 A011713
%Y A011710 Sequence in context: A011716 A011713 A011699 this_sequence A135500 A023972 A103674
%K A011710 nonn
%O A011710 0,1
%A A011710 njas

%I A135500
%S A135500 0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,
%T A135500 0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,
%U A135500 1,1,1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,0,0
%N A135500 Generating function for Viswanath's constant, using the golden string.
%C A135500 For each bit of the golden string that is a 1, write seven consecutive bits, and for each 0 of the golden string write eight consecutive bits.
%C A135500 Alternate between 0 and 1. Exclude the first seven bits since we are based at zero, just like the golden string. Heads = 1, Tails = 0.
%H A135500 S. Findley, <a href="http://groups.myspace.com/ViswanathsCurve">Viswanath's curve</a>
%F A135500 Each power of Viswanath's constant (1.131988248...) And V^3 has a coresponding coin flip. Simply take the absolute values of the two possible(+Heads or -Tails) outcomes, and choose the flip closest to the value of the power.
%e A135500 Bit 1 of the golden string is a 1, so bits 8-14(seven consecutive) are the same. Bit 2 of the golden string is 0, so bits 15-22(eight consecutive) are the same. Odd bits of the golden string mean to write 1, and even bits of the golden string mean to write 0.
%o A135500 'Visual Basic .NET
%o A135500 Private Structure VISINFO
%o A135500 Public dec, str, terms As String
%o A135500 End Structure
%o A135500 Private Function InputDecimal(ByVal vConstant As String) As VISINFO
%o A135500 On Error Resume Next
%o A135500 Dim i, q As Int32, a, b, c, n, z, v, sum As Decimal, gBit As String
%o A135500 gBit = "" : a = 0 : b = 1 : c = 0 : n = CDec(CDec(vConstant) ^ 3) : z = n
%o A135500 InputDecimal.dec = "" : InputDecimal.terms = "" : InputDecimal.str = ""
%o A135500 For i = 1 To CInt(txtExponent.Text)
%o A135500 If Abs(Abs(a + b) - n) &lt; Abs(Abs(a - b) - n) Then
%o A135500 c = a + b : gBit = "1"
%o A135500 Else
%o A135500 c = a - b : gBit = "0"
%o A135500 End If
%o A135500 a = b : b = c
%o A135500 v = CDec(System.Math.Abs(c) ^ (1 / i))
%o A135500 sum += v : q += 1
%o A135500 InputDecimal.terms &= gBit & " " & CStr(i) & " " & CStr(System.Math.Round(n)) & " " & c.ToString & vbCrLf
%o A135500 InputDecimal.str &= gBit
%o A135500 InputDecimal.dec = ((sum / q) ^ (1 / 3)).ToString
%o A135500 n = n * z
%o A135500 Next
%o A135500 End Function
%Y A135500 Cf. A036299, A078416, A115064.
%Y A135500 Adjacent sequences: A135497 A135498 A135499 this_sequence A135501 A135502 A135503
%Y A135500 Sequence in context: A011713 A011699 A011710 this_sequence A023972 A103674 A044937
%K A135500 easy,nonn,uned
%O A135500 0,1
%A A135500 Shane Findley (divineprime(AT)yahoo.com), Feb 19 2008

%I A023972
%S A023972 0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,
%T A023972 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U A023972 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1
%N A023972 First bit in fractional part of binary expansion of 5-th root of n.
%t A023972 Array[ Function[ n, RealDigits[ N[ Power[ n, 1/5 ], 10 ], 2 ]// (#[ [ 1, #[ [ 2 ] ]+1 ] ])& ], 110 ]
%Y A023972 Adjacent sequences: A023969 A023970 A023971 this_sequence A023973 A023974 A023975
%Y A023972 Sequence in context: A011699 A011710 A135500 this_sequence A103674 A044937 A025459
%K A023972 nonn,base
%O A023972 1,1
%A A023972 njas, Olivier Gerard (ogerard(AT)ext.jussieu.fr)

%I A103674
%S A103674 0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,1,1,1,0,0,
%T A103674 0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,1,0,0,1,0,0,0,0,0,0,1,0,0,0,0,
%U A103674 0,1,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,1,1,0,0,0,1,0,0,1,0,0
%N A103674 If in binary representation n! contains 6! then 1 else 0.
%C A103674 a(A103678(n)) = 1, a(A103679(n)) = 0.
%H A103674 <a href="http://www.research.att.com/~njas/sequences/Sindx_Fa.html#factorial">Index entries for sequences related to factorial numbers</a>
%H A103674 <a href="http://www.research.att.com/~njas/sequences/Sindx_Bi.html#binary">Index entries for sequences related to binary expansion of n</a>
%Y A103674 Cf. A102730, A036603, A007088, A000142, A103673, A103675.
%Y A103674 Adjacent sequences: A103671 A103672 A103673 this_sequence A103675 A103676 A103677
%Y A103674 Sequence in context: A011710 A135500 A023972 this_sequence A044937 A025459 A079365
%K A103674 nonn
%O A103674 0,1
%A A103674 Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Feb 12 2005

%I A044937
%S A044937 0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,
%T A044937 0,0,0,0,1,1,0,0,0,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0,0,
%U A044937 0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,1,1,1,0
%N A044937 Number of runs of even length in base 6 representation of n.
%Y A044937 Adjacent sequences: A044934 A044935 A044936 this_sequence A044938 A044939 A044940
%Y A044937 Sequence in context: A135500 A023972 A103674 this_sequence A025459 A079365 A037822
%K A044937 nonn,base
%O A044937 1,1
%A A044937 Clark Kimberling (ck6(AT)evansville.edu)

%I A025459
%S A025459 0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,
%T A025459 0,0,0,1,0,1,0,0,0,0,1,0,1,0,0,0,0,1,0,0,0,0,1,0,1,0,0,0,0,1,0,1,0,1,0,0,
%U A025459 1,0,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0,1,1,0,0
%N A025459 Number of partitions of n into 6 positive cubes.
%Y A025459 Adjacent sequences: A025456 A025457 A025458 this_sequence A025460 A025461 A025462
%Y A025459 Sequence in context: A023972 A103674 A044937 this_sequence A079365 A037822 A005088
%K A025459 nonn
%O A025459 0,1
%A A025459 David W. Wilson (davidwwilson(AT)comcast.net)

%I A079365
%S A079365 0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,1,1,0,0,0,1,0,0,0,0,1,1,0,1,
%T A079365 0,0,0,1,1,1,1,1,1,0,0,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0,0,0
%N A079365 Binary expansion of the Chaitin Omega number Omega_U.
%C A079365 This is the halting probability of a certain universal Chaitin (self-delimiting Turing) machine U.
%C A079365 The full (infinite precision) number is random and noncomputable.
%D A079365 C. C. Calude, M. J. Dinneen and C.-K. Shu, Computing a glimpse of randomness, Exper. Math., 11 (2002), 361-370.
%H A079365 C. C. Calude, M. J. Dinneen and C.-K. Shu, <a href="http://www.expmath.org/expmath/volumes/11/11.html">Computing a glimpse of randomness</a>, Exper. Math., 11 (2002), 361-370.
%H A079365 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ChaitinsConstant.html">Chaitin's Constant</a>
%Y A079365 Adjacent sequences: A079362 A079363 A079364 this_sequence A079366 A079367 A079368
%Y A079365 Sequence in context: A103674 A044937 A025459 this_sequence A037822 A005088 A011686
%K A079365 nonn,nice,cons,base,hard
%O A079365 0,1
%A A079365 njas, Feb 15 2003

%I A037822
%S A037822 0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,0,0,1,1,1,0,0,0,0,1,1,1,
%T A037822 1,0,0,0,1,1,1,1,1,0,0,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,
%U A037822 0,0,1,1,0,0,0,0,0,1,1,1,0,0,0,0,1,1,1,1,0,0,0,1,1,1,1,1,0,0
%N A037822 Number of i such that d(i)<d(i-1), where Sum{d(i)*7^i: i=0,1,....,m} is base 7 representation of n.
%Y A037822 Adjacent sequences: A037819 A037820 A037821 this_sequence A037823 A037824 A037825
%Y A037822 Sequence in context: A044937 A025459 A079365 this_sequence A005088 A011686 A070108
%K A037822 nonn,base
%O A037822 1,1
%A A037822 Clark Kimberling (ck6(AT)evansville.edu)

%I A005088
%S A005088 0,0,0,0,0,0,1,0,0,0,0,0,1,1,0,0,0,0,1,0,1,0,0,0,0,1,0,
%T A005088 1,0,0,1,0,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0,1,0,0,
%U A005088 0,1,1,0,0,0,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,1,1,1,1,0,0
%N A005088 Number of primes = 1 mod 3 dividing n.
%H A005088 S. R. Finch and Pascal Sebah, <a href="http://arXiv.org/abs/math.NT/0604465">Squares and Cubes Modulo n</a> (arXiv: math.NT/0604465).
%F A005088 Additive with a(p^e) = 1 if p = 1 (mod 3), 0 otherwise.
%Y A005088 Adjacent sequences: A005085 A005086 A005087 this_sequence A005089 A005090 A005091
%Y A005088 Sequence in context: A025459 A079365 A037822 this_sequence A011686 A070108 A011675
%K A005088 nonn
%O A005088 1,1
%A A005088 njas

%I A011686
%S A011686 0,0,0,0,0,0,1,0,0,0,0,0,1,1,0,0,0,0,1,0,1,0,0,0,1,1,1,
%T A011686 1,0,0,1,0,0,0,1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,1,1,1,1,1,
%U A011686 0,1,0,0,0,0,1,1,1,0,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,1
%N A011686 A binary m-sequence: expansion of reciprocal of x^7+x^6+1.
%D A011686 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011686 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011686 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011686 Adjacent sequences: A011683 A011684 A011685 this_sequence A011687 A011688 A011689
%Y A011686 Sequence in context: A079365 A037822 A005088 this_sequence A070108 A011675 A011687
%K A011686 nonn
%O A011686 0,1
%A A011686 njas

%I A070108
%S A070108 0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,
%T A070108 0,0,0,1,0,1,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,0,1,0,
%U A070108 0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,1,0,1,0
%N A070108 Number of integer triangles with perimeter n and prime side lengths which are obtuse and isosceles.
%H A070108 R. Zumkeller, <a href="http://www.research.att.com/~njas/sequences/a070080.txt">Integer-sided triangles</a>
%e A070108 a(k)<=1 until k = 140, for k = 141 there are A005044(141)=432 integer triangles, a(141)=2 as
%e A070108 [37=37<67]: 37+37+67 = 141 and 2*(37^2)<67^2 and 37, 67 are primes,
%e A070108 [41=41<59]: 41+41+59 = 141 and 2*(41^2)<59^2 and 41, 59 are primes.
%Y A070108 Cf. A070080, A070081, A070082, A070101, A059169, A070088, A070092, A070103, A070106, A070135.
%Y A070108 Adjacent sequences: A070105 A070106 A070107 this_sequence A070109 A070110 A070111
%Y A070108 Sequence in context: A037822 A005088 A011686 this_sequence A011675 A011687 A011690
%K A070108 nonn
%O A070108 1,1
%A A070108 Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), May 05 2002

%I A011675
%S A011675 0,0,0,0,0,0,1,0,0,0,1,0,0,1,1,0,0,0,1,0,1,1,1,0,1,0,1,
%T A011675 1,0,1,1,0,0,0,0,0,1,1,0,0,1,1,0,1,0,1,0,0,1,1,1,0,0,1,
%U A011675 1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0
%N A011675 A binary m-sequence: expansion of reciprocal of x^7+x^4+1.
%D A011675 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011675 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011675 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011675 Adjacent sequences: A011672 A011673 A011674 this_sequence A011676 A011677 A011678
%Y A011675 Sequence in context: A005088 A011686 A070108 this_sequence A011687 A011690 A011688
%K A011675 nonn
%O A011675 0,1
%A A011675 njas

%I A011687
%S A011687 0,0,0,0,0,0,1,0,0,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,
%T A011687 0,1,1,1,1,0,1,1,0,1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,1,
%U A011687 0,1,1,0,0,0,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,1,1
%N A011687 A binary m-sequence: expansion of reciprocal of x^7+x^6+x^5+x^4+1.
%D A011687 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011687 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011687 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011687 Adjacent sequences: A011684 A011685 A011686 this_sequence A011688 A011689 A011690
%Y A011687 Sequence in context: A011686 A070108 A011675 this_sequence A011690 A011688 A011676
%K A011687 nonn
%O A011687 0,1
%A A011687 njas

%I A011690
%S A011690 0,0,0,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0,1,1,1,1,0,1,1,1,0,
%T A011690 0,0,0,1,1,1,1,1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0,
%U A011690 1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0,1,1,0,1,1,1,1,0
%N A011690 A binary m-sequence: expansion of reciprocal of x^7+x^3+1.
%D A011690 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011690 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011690 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011690 Adjacent sequences: A011687 A011688 A011689 this_sequence A011691 A011692 A011693
%Y A011690 Sequence in context: A070108 A011675 A011687 this_sequence A011688 A011676 A011691
%K A011690 nonn
%O A011690 0,1
%A A011690 njas

%I A011688
%S A011688 0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,1,
%T A011688 1,1,0,0,1,1,0,0,1,0,1,0,0,0,1,0,0,0,1,1,0,0,0,0,1,1,1,
%U A011688 1,0,1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,1,1
%N A011688 A binary m-sequence: expansion of reciprocal of x^7+x^5+x^4+x^3+1.
%D A011688 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011688 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011688 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011688 Adjacent sequences: A011685 A011686 A011687 this_sequence A011689 A011690 A011691
%Y A011688 Sequence in context: A011675 A011687 A011690 this_sequence A011676 A011691 A011684
%K A011688 nonn
%O A011688 0,1
%A A011688 njas

%I A011676
%S A011676 0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,0,1,1,0,0,1,0,0,0,0,0,1,
%T A011676 1,1,1,0,0,0,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0,0,0,1,0,0,1,
%U A011676 1,1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0
%N A011676 A binary m-sequence: expansion of reciprocal of x^7+x^6+x^4+x^2+1.
%D A011676 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011676 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011676 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011676 Adjacent sequences: A011673 A011674 A011675 this_sequence A011677 A011678 A011679
%Y A011676 Sequence in context: A011687 A011690 A011688 this_sequence A011691 A011684 A011674
%K A011676 nonn
%O A011676 0,1
%A A011676 njas

%I A011691
%S A011691 0,0,0,0,0,0,1,0,1,0,1,1,0,1,1,1,1,1,1,1,0,0,1,1,0,1,1,
%T A011691 0,1,0,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,0,1,1,1,1,0,0,0,1,
%U A011691 1,1,0,1,1,1,0,1,0,1,1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0
%N A011691 A binary m-sequence: expansion of reciprocal of x^7+x^6+x^5+x^2+1.
%D A011691 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011691 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011691 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011691 Adjacent sequences: A011688 A011689 A011690 this_sequence A011692 A011693 A011694
%Y A011691 Sequence in context: A011690 A011688 A011676 this_sequence A011684 A011674 A011683
%K A011691 nonn
%O A011691 0,1
%A A011691 njas

%I A011684
%S A011684 0,0,0,0,0,0,1,0,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0,0,1,0,0,
%T A011684 1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,1,0,1,1,1,0,1,1,0,1,1,1,
%U A011684 0,0,1,1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,1,1,1,1,0,1,1,1
%N A011684 A binary m-sequence: expansion of reciprocal of x^7+x^4+x^3+x^2+1.
%D A011684 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011684 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011684 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011684 Adjacent sequences: A011681 A011682 A011683 this_sequence A011685 A011686 A011687
%Y A011684 Sequence in context: A011688 A011676 A011691 this_sequence A011674 A011683 A011681
%K A011684 nonn
%O A011684 0,1
%A A011684 njas

%I A011674
%S A011674 0,0,0,0,0,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0,0,0,0,1,1,1,
%T A011674 0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0,0,1,1,0,1,1,1,0,1,0,
%U A011674 0,0,1,0,0,0,1,1,0,1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,1
%N A011674 A binary m-sequence: expansion of reciprocal of x^7+x^6+x^5+x^4+x^3+x^2+1.
%D A011674 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011674 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011674 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011674 Adjacent sequences: A011671 A011672 A011673 this_sequence A011675 A011676 A011677
%Y A011674 Sequence in context: A011676 A011691 A011684 this_sequence A011683 A011681 A011689
%K A011674 nonn
%O A011674 0,1
%A A011674 njas

%I A011683
%S A011683 0,0,0,0,0,0,1,1,0,0,0,0,1,0,0,1,0,0,1,1,1,1,1,1,1,0,1,
%T A011683 1,1,1,1,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,1,1,0,
%U A011683 1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1
%N A011683 A binary m-sequence: expansion of reciprocal of x^7+x^5+x^4+x^3+x^2+x+1.
%D A011683 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011683 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011683 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011683 Adjacent sequences: A011680 A011681 A011682 this_sequence A011684 A011685 A011686
%Y A011683 Sequence in context: A011691 A011684 A011674 this_sequence A011681 A011689 A011680
%K A011683 nonn
%O A011683 0,1
%A A011683 njas

%I A011681
%S A011681 0,0,0,0,0,0,1,1,0,0,1,0,1,0,0,0,1,1,1,0,0,0,0,1,1,1,1,
%T A011681 1,0,0,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0,1,1,0,
%U A011681 1,1,1,1,1,1,1,0,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,1,0,1
%N A011681 A binary m-sequence: expansion of reciprocal of x^7+x^6+x^5+x^3+x^2+x+1.
%D A011681 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011681 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011681 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011681 Adjacent sequences: A011678 A011679 A011680 this_sequence A011682 A011683 A011684
%Y A011681 Sequence in context: A011684 A011674 A011683 this_sequence A011689 A011680 A011677
%K A011681 nonn
%O A011681 0,1
%A A011681 njas

%I A011689
%S A011689 0,0,0,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,1,0,0,1,1,1,0,
%T A011689 1,0,1,1,1,0,0,0,0,1,0,0,1,1,0,0,0,0,0,1,0,1,0,1,0,1,1,
%U A011689 0,1,0,0,1,0,0,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0,1,1,0,1,0
%N A011689 A binary m-sequence: expansion of reciprocal of x^7+x^3+x^2+x+1.
%D A011689 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011689 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%D A011689 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%Y A011689 Adjacent sequences: A011686 A011687 A011688 this_sequence A011690 A011691 A011692
%Y A011689 Sequence in context: A011674 A011683 A011681 this_sequence A011680 A011677 A011685
%K A011689 nonn
%O A011689 0,1
%A A011689 njas

%I A011680
%S A011680 0,0,0,0,0,0,1,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,
%T A011680 1,1,1,0,0,1,0,0,0,0,1,0,0,0,1,0,0,1,0,0,1,1,1,1,0,1,0,
%U A011680 1,0,0,0,0,0,1,0,1,1,1,1,0,0,1,1,1,0,1,1,1,1,1,1,1,0,1
%N A011680 A binary m-sequence: expansion of reciprocal of x^7+x^6+x^5+x^4+x^2+x+1.
%D A011680 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011680 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011680 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011680 Adjacent sequences: A011677 A011678 A011679 this_sequence A011681 A011682 A011683
%Y A011680 Sequence in context: A011683 A011681 A011689 this_sequence A011677 A011685 A011678
%K A011680 nonn
%O A011680 0,1
%A A011680 njas

%I A011677
%S A011677 0,0,0,0,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0,0,
%T A011677 1,0,0,0,0,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0,0,1,1,1,0,0,1,
%U A011677 0,1,0,0,1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,1,1,1,0,1,1,1,0
%N A011677 A binary m-sequence: expansion of reciprocal of x^7+x^5+x^2+x+1.
%D A011677 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011677 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011677 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011677 Adjacent sequences: A011674 A011675 A011676 this_sequence A011678 A011679 A011680
%Y A011677 Sequence in context: A011681 A011689 A011680 this_sequence A011685 A011678 A011679
%K A011677 nonn
%O A011677 0,1
%A A011677 njas

%I A011685
%S A011685 0,0,0,0,0,0,1,1,1,0,1,0,1,0,0,0,1,0,1,1,1,0,0,0,1,1,1,
%T A011685 1,0,1,1,1,0,1,1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,
%U A011685 0,1,1,0,1,0,0,0,0,1,0,1,0,0,1,0,1,1,0,1,1,0,0,1,0,1,0
%N A011685 A binary m-sequence: expansion of reciprocal of x^7+x^6+x^3+x+1.
%D A011685 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011685 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011685 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011685 Adjacent sequences: A011682 A011683 A011684 this_sequence A011686 A011687 A011688
%Y A011685 Sequence in context: A011689 A011680 A011677 this_sequence A011678 A011679 A011682
%K A011685 nonn
%O A011685 0,1
%A A011685 njas

%I A011678
%S A011678 0,0,0,0,0,0,1,1,1,0,1,1,0,1,1,1,1,1,0,0,1,1,1,1,1,1,1,
%T A011678 0,1,0,0,1,0,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,
%U A011678 0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0,1,0,1,1,1,1,0,1,1,1,0
%N A011678 A binary m-sequence: expansion of reciprocal of x^7+x^5+x^3+x+1.
%D A011678 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011678 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011678 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011678 Adjacent sequences: A011675 A011676 A011677 this_sequence A011679 A011680 A011681
%Y A011678 Sequence in context: A011680 A011677 A011685 this_sequence A011679 A011682 A078926
%K A011678 nonn
%O A011678 0,1
%A A011678 njas

%I A011679
%S A011679 0,0,0,0,0,0,1,1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0,1,
%T A011679 1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0,1,1,0,1,0,1,
%U A011679 0,1,0,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0,0,1,0,1,1,0,0,0
%N A011679 A binary m-sequence: expansion of reciprocal of x^7+x^6+x^4+x+1.
%D A011679 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011679 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011679 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011679 Adjacent sequences: A011676 A011677 A011678 this_sequence A011680 A011681 A011682
%Y A011679 Sequence in context: A011677 A011685 A011678 this_sequence A011682 A078926 A025458
%K A011679 nonn
%O A011679 0,1
%A A011679 njas

%I A011682
%S A011682 0,0,0,0,0,0,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,
%T A011682 1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,1,0,1,1,1,1,0,1,1,0,
%U A011682 1,0,1,1,0,1,1,0,0,1,0,0,1,0,0,0,1,1,1,0,0,0,0,1,0,1,1
%N A011682 A binary m-sequence: expansion of reciprocal of x^7+x+1.
%D A011682 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011682 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011682 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011682 Adjacent sequences: A011679 A011680 A011681 this_sequence A011683 A011684 A011685
%Y A011682 Sequence in context: A011685 A011678 A011679 this_sequence A078926 A025458 A093958
%K A011682 nonn
%O A011682 0,1
%A A011682 njas

%I A078926
%S A078926 0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,
%T A078926 0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,
%U A078926 0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,1,0
%N A078926 Number of primitive Pythagorean triangles with perimeter 2n.
%C A078926 A Pythagorean triangle is a right triangle whose edge lengths are all integers; such a triangle is 'primitive' if the lengths are relatively prime.
%C A078926 Equivalently, number of odd unitary divisors d of n such that sqrt(n) < d < sqrt(2n). (A divisor d of n is 'unitary' if gcd(d,n/d) = 1.) Sketch of proof: A primitive Pythagorean triangle has edge lengths (r^2-s^2, 2rs, r^2+s^2), where 1<=s<r, r and s are relatively prime and r+s is odd. This has perimeter 2n iff n=r(r+s). Let d=r+s.
%e A078926 a(858)=2; the primitive Pythagorean triangles with edge lengths (364, 627, 725) and (195, 748, 773) both have perimeter 2*858 = 1716.
%t A078926 oddpart[n_] := If[OddQ[n], n, oddpart[n/2]]; a[n_] := Length[Select[Divisors[oddpart[n]], n<#^2<2n&&GCD[ #, n/# ]==1&]]
%Y A078926 a(n) = A070109(2n). A078927(n) is smallest s such that a(s)=n. a(n) is nonzero iff n is in A020886.
%Y A078926 Adjacent sequences: A078923 A078924 A078925 this_sequence A078927 A078928 A078929
%Y A078926 Sequence in context: A011678 A011679 A011682 this_sequence A025458 A093958 A044936
%K A078926 nonn,easy
%O A078926 1,1
%A A078926 Dean Hickerson (dean(AT)math.ucdavis.edu), Dec 15 2002

%I A025458
%S A025458 0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,
%T A025458 0,0,1,0,1,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,0,0,1,0,0,0,1,0,0,1,
%U A025458 0,0,0,1,0,0,1,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0,0,0,0,0,0
%N A025458 Number of partitions of n into 5 positive cubes.
%Y A025458 Adjacent sequences: A025455 A025456 A025457 this_sequence A025459 A025460 A025461
%Y A025458 Sequence in context: A011679 A011682 A078926 this_sequence A093958 A044936 A133944
%K A025458 nonn
%O A025458 0,1
%A A025458 David W. Wilson (davidwwilson(AT)comcast.net)

%I A093958
%S A093958 0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,1,0,0,0,0,
%T A093958 0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,1,0,0,0,0,0,1,0,0,
%U A093958 0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,1,0,0,0,0,0,1
%N A093958 A091844(n) - 4.
%C A093958 The purpose of A093955-A093958 is to compare A090822, A091787, A091799 and A091844 on the same "scale".
%C A093958 Sequence is unbounded.
%H A093958 F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and A. R. Wilks, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">A Slow-Growing Sequence Defined by an Unusual Recurrence</a>, J. Integer Sequences, Vol. 10 (2007), #07.1.2.
%H A093958 F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and A. R. Wilks, A Slow-Growing Sequence Defined by an Unusual Recurrence [<a href="http://www.research.att.com/~njas/doc/gijs.pdf">pdf</a>, <a href="http://www.research.att.com/~njas/doc/gijs.ps">ps</a>].
%Y A093958 Cf. A090822, A093955-A093958.
%Y A093958 Adjacent sequences: A093955 A093956 A093957 this_sequence A093959 A093960 A093961
%Y A093958 Sequence in context: A011682 A078926 A025458 this_sequence A044936 A133944 A052434
%K A093958 nonn
%O A093958 1,1
%A A093958 njas, May 22 2004

%I A044936
%S A044936 0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,1,0,0,0,0,1,
%T A044936 0,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,1,0,0,0,0,0,1,0,0,0,1,
%U A044936 1,0,1,1,0,0,0,1,0,0,0,0,0,1,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,1
%N A044936 Number of runs of even length in base 5 representation of n.
%Y A044936 Adjacent sequences: A044933 A044934 A044935 this_sequence A044937 A044938 A044939
%Y A044936 Sequence in context: A078926 A025458 A093958 this_sequence A133944 A052434 A094912
%K A044936 nonn,base
%O A044936 1,1
%A A044936 Clark Kimberling (ck6(AT)evansville.edu)

%I A133944
%S A133944 0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,
%T A133944 1,0,0,0,1,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,
%U A133944 0,1,0,0,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0
%V A133944 0,0,0,0,0,-1,0,0,0,0,0,-1,0,0,0,0,0,-1,0,-1,0,0,0,-1,0,0,0,0,0,-1,0,0,0,0,0,-1,0,0,0,
%W A133944 -1,0,-1,0,0,0,0,0,-1,0,0,0,0,0,-1,0,-1,0,0,0,-1,0,0,0,0,0,-1,0,0,0,0,0,-1,0,0,0,0,0,
%X A133944 -1,0,-1,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,-1,0,-1,0,0,0,0,0,-1,0,0,0,-1,0,-1,0
%N A133944 Sum mu(k), where the sum is over the integers k which are the "non-isolated divisors" of n and mu(k) is the Moebius function (mu(k) = A008683(k)). A positive divisor, k, of n is non-isolated if (k-1) and/or (k+1) also divides n.
%C A133944 A133943(n) = -A133944(n), for n >= 2.
%p A133944 A133944 := proc(n) local divs,k,i,a ; divs := convert(numtheory[divisors](n),list) ; a := 0 ; for i from 1 to nops(divs) do k := op(i,divs) ; if k-1 in divs or k+1 in divs then a := a+numtheory[mobius](k) ; fi ; od: RETURN(a) ; end: seq(A133944(n),n=1..120) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 21 2007
%Y A133944 Cf. A133943.
%Y A133944 Adjacent sequences: A133941 A133942 A133943 this_sequence A133945 A133946 A133947
%Y A133944 Sequence in context: A025458 A093958 A044936 this_sequence A052434 A094912 A103673
%K A133944 sign
%O A133944 1,1
%A A133944 Leroy Quet (qq-quet(AT)mindspring.com), Sep 30 2007
%E A133944 More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 21 2007

%I A052434
%S A052434 0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,1,0,0,1,0,0,0,0,1,0,0,1,0,0,0,0,1,
%T A052434 0,0,0,1,0,0,1,0,0,0,1,1,0,0,0,0,0,0,0,0,1,1,0,0,1,0,0,0,0,1,0,0,0,0,0,
%U A052434 0,1,1,1,0,0,0,1,0,0,0,1,1,0,0,0,0,1,0,0,0,0,0,1,1,0,0,0,1,0,0,1
%V A052434 0,0,0,0,0,-1,0,0,0,0,0,-1,0,0,0,0,0,-1,-1,0,0,-1,0,0,0,0,1,0,0,-1,0,0,0,0,
%W A052434 1,0,0,0,1,0,0,-1,0,0,0,-1,-1,0,0,0,0,0,0,0,0,1,1,0,0,-1,0,0,0,0,1,0,0,0,
%X A052434 0,0,0,-1,-1,-1,0,0,0,-1,0,0,0,-1,-1,0,0,0,0,-1,0,0,0,0,0,1,1,0,0,0,1,0,0,-1
%N A052434 Round[R[x]-PrimePi[x]], where R[x] is the Riemann prime number formula.
%H A052434 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeCountingFunction.html">Link to a section of The World of Mathematics.</a>
%Y A052434 Cf. A052435.
%Y A052434 Adjacent sequences: A052431 A052432 A052433 this_sequence A052435 A052436 A052437
%Y A052434 Sequence in context: A093958 A044936 A133944 this_sequence A094912 A103673 A028862
%K A052434 sign
%O A052434 2,1
%A A052434 Eric Weisstein (eric(AT)weisstein.com)

%I A094912
%S A094912 0,0,0,0,0,1,0,0,0,0,1,0,0,1,0,0,0,0,0,0,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,
%T A094912 0,0,0,0,0,1,1,0,1,0,0,1,0,0,0,0,0,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0,
%U A094912 0,0,0,0,0,0,0,0,0,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,1
%N A094912 a(n) = output produced by a finite automaton when fed binary representation of n, read from right to left.
%C A094912 There are 3 states. Start in state A.
%C A094912 If in A and 0 arrives go to A
%C A094912 If in A and 1 arrives go to B
%C A094912 If in B and 0 arrives go to C
%C A094912 If in B and 1 arrives go to A
%C A094912 If in C and 0 arrives go to A
%C A094912 If in C and 1 arrives go to C
%C A094912 If end in A, B, C then output 0, 0, 1 respectively.
%H A094912 J.-P. Allouche and M. Mendes France, <a href="http://www.lri.fr/~allouche/">Automata and Automatic Sequences</a>, see example, pages 12-13.
%e A094912 a(10) = 1: 10 = 1010, read from right: A->A->B->C, so output a 1.
%o A094912 (PARI) {m=104;for(n=0,m,tape=binary(n);d=length(tape);state="A";for(j=0,d-1,in=tape[d-j];
%o A094912 state=if(state=="A",if(in==0,"A","B"),if(state=="B",if(in==0,"C","A"),if(in==0,"A","C"))));
%o A094912 print1(if(state=="A"||state=="B",0,1),","))} - Klaus Brockhaus, Jun 23 2004
%Y A094912 Adjacent sequences: A094909 A094910 A094911 this_sequence A094913 A094914 A094915
%Y A094912 Sequence in context: A044936 A133944 A052434 this_sequence A103673 A028862 A011673
%K A094912 nonn,easy
%O A094912 0,1
%A A094912 njas, Jun 21 2004
%E A094912 A very interesting paper. I only looked though it as far as page 12. Perhaps some reader would read to the end and add appropriate references to it from other entries in the OEIS, as well as adding any new sequences that are found. A similar remark could be made about many papers on Jean-Paul Allouche's web site. - njas
%E A094912 More terms from Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jun 23 2004

%I A103673
%S A103673 0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,1,1,0,1,0,1,0,1,0,0,0,1,1,
%T A103673 1,0,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,0,1,1,1,1,0,1,1,1,1,1,1,0,1,1,1,1,
%U A103673 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%N A103673 If in binary representation n! contains 5! then 1 else 0.
%C A103673 a(A103676(n)) = 1, a(A103677(n)) = 0.
%H A103673 <a href="http://www.research.att.com/~njas/sequences/Sindx_Fa.html#factorial">Index entries for sequences related to factorial numbers</a>
%H A103673 <a href="http://www.research.att.com/~njas/sequences/Sindx_Bi.html#binary">Index entries for sequences related to binary expansion of n</a>
%Y A103673 Cf. A102730, A036603, A007088, A000142, A103674, A103675.
%Y A103673 Adjacent sequences: A103670 A103671 A103672 this_sequence A103674 A103675 A103676
%Y A103673 Sequence in context: A133944 A052434 A094912 this_sequence A028862 A011673 A104853
%K A103673 nonn
%O A103673 0,1
%A A103673 Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Feb 12 2005

%I A028862
%S A028862 0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,0,0,0,0,0,1,0,1,1,1,1,0,
%T A028862 1,0,0,0,0,1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,
%U A028862 0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,1,1,0,1,1,1,1,0,0,1,1
%V A028862 0,0,0,0,0,-1,0,0,0,0,-1,0,-1,0,0,0,0,0,0,0,-1,0,-1,-1,-1,-1,0,
%W A028862 -1,0,0,0,0,-1,0,-1,-1,0,-1,0,0,-1,-1,-1,0,-1,0,0,-1,0,0,0,-1,-1,-1,
%X A028862 0,-1,0,0,-1,0,0,-1,-1,0,-1,0,0,0,-1,-1,-1,-1,0,-1,-1,-1,-1,0,0,-1,-1
%N A028862 [ sin(Fibonacci(n)) ].
%Y A028862 Adjacent sequences: A028859 A028860 A028861 this_sequence A028863 A028864 A028865
%Y A028862 Sequence in context: A052434 A094912 A103673 this_sequence A011673 A104853 A079872
%K A028862 sign
%O A028862 0,1
%A A028862 njas

%I A011673
%S A011673 0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,1,0,0,1,1,1,1,0,1,0,
%T A011673 0,0,1,1,1,0,0,1,0,0,1,0,1,1,0,1,1,1,0,1,1,0,0,1,1,0,1,
%U A011673 0,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,1
%N A011673 A binary m-sequence: expansion of reciprocal of x^6+x^5+1.
%D A011673 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011673 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011673 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%H A011673 Michael Gilleland, <a href="http://www.research.att.com/~njas/sequences/selfsimilar.html">Some Self-Similar Integer Sequences</a>
%Y A011673 Adjacent sequences: A011670 A011671 A011672 this_sequence A011674 A011675 A011676
%Y A011673 Sequence in context: A094912 A103673 A028862 this_sequence A104853 A079872 A011672
%K A011673 nonn
%O A011673 0,1
%A A011673 njas

%I A104853
%S A104853 0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
%T A104853 0,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,
%U A104853 0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0
%N A104853 Binary array below read by downward antidiagonals.
%C A104853 The k-th row has alternating blocks of 2^k - k 0's followed by k 1's.
%C A104853 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
%C A104853 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, ...
%C A104853 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, ...
%C A104853 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, ...
%C A104853 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, ...
%C A104853 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
%C A104853 ...
%C A104853 The n-th column sum is A103863(n) : 0, 1, 1, 2, 0, 2, 2, 3, 0, 1, 1, 2, 1, 3, ...
%D A104853 David Applegate, Benoit Cloitre, Philippe DELEHAM and N. J. A. Sloane, Sloping binary numbers : a new sequence related to the binary numbers, J. Integer Seq. 8 (2005), no. 3, Article 05.3.6, 15 pp.
%H A104853 David Applegate, Benoit Cloitre, Philippe DELEHAM and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [<a href="http://www.research.att.com/~njas/doc/slopey.pdf">pdf</a>, <a href="http://www.research.att.com/~njas/doc/slopey.ps">ps</a>].
%Y A104853 Cf. A102370, A103863.
%Y A104853 Adjacent sequences: A104850 A104851 A104852 this_sequence A104854 A104855 A104856
%Y A104853 Sequence in context: A103673 A028862 A011673 this_sequence A079872 A011672 A011671
%K A104853 nonn,easy,tabl
%O A104853 0,1
%A A104853 Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Apr 23 2005

%I A079872
%S A079872 0,0,0,0,0,1,0,0,0,1,0,1,0,1,1,0,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,
%T A079872 1,0,1,1,1,0,1,0,1,1,1,0,1,0,1,1,1,0,1,1,1,1,1,0,1,0,1,1,0,1,1,0,1,1,1,
%U A079872 0,1,0,1,1,1,1,1,0,1,0,1,0,1,1,1,1,1,0,1,1,1,1,1,1,1
%V A079872 0,0,0,0,0,-1,0,0,0,-1,0,-1,0,1,1,0,0,1,0,1,1,1,0,-1,0,-1,0,-1,0,-1,0,0,1,1,1,-1,0,-1,
%W A079872 -1,1,0,-1,0,1,1,1,0,-1,0,1,-1,1,0,1,-1,1,1,1,0,1,0,1,1,0,-1,-1,0,-1,-1,-1,0,-1,0,1,-1,
%X A079872 -1,1,-1,0,-1,0,-1,0,-1,-1,-1,-1,-1,0,-1,1,1,1,1,1,-1
%N A079872 signum(round(n^(1/Omega(n)))^Omega(n) - n), where Omega(n) is the total number of prime factors of n (A001222).
%C A079872 a(m) = 0 iff m is a prime power (A000961).
%Y A079872 a(n)=A057427(A079869(n) - n).
%Y A079872 Adjacent sequences: A079869 A079870 A079871 this_sequence A079873 A079874 A079875
%Y A079872 Sequence in context: A028862 A011673 A104853 this_sequence A011672 A011671 A086483
%K A079872 sign
%O A079872 1,1
%A A079872 Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Jan 13 2003

%I A011672
%S A011672 0,0,0,0,0,1,0,0,1,0,0,0,0,0,1,0,0,1,0,0,0,0,0,1,0,0,1,
%T A011672 0,0,0,0,0,1,0,0,1,0,0,0,0,0,1,0,0,1,0,0,0,0,0,1,0,0,1,
%U A011672 0,0,0,0,0,1,0,0,1,0,0,0,0,0,1,0,0,1,0,0,0,0,0,1,0,0,1
%N A011672 Expansion of reciprocal of x^6+x^3+1 (mod 2).
%Y A011672 Adjacent sequences: A011669 A011670 A011671 this_sequence A011673 A011674 A011675
%Y A011672 Sequence in context: A011673 A104853 A079872 this_sequence A011671 A086483 A011667
%K A011672 nonn
%O A011672 0,1
%A A011672 njas

%I A011671
%S A011671 0,0,0,0,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,1,1,0,0,0,0,0,1,
%T A011671 0,1,0,0,1,0,0,1,1,0,0,1,0,1,1,0,0,0,0,0,1,0,1,0,0,1,0,
%U A011671 0,1,1,0,0,1,0,1,1,0,0,0,0,0,1,0,1,0,0,1,0,0,1,1,0,0,1
%N A011671 A binary m-sequence: expansion of reciprocal of x^6+x^5+x^4+x^2+1.
%D A011671 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011671 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011671 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%H A011671 Michael Gilleland, <a href="http://www.research.att.com/~njas/sequences/selfsimilar.html">Some Self-Similar Integer Sequences</a>
%Y A011671 Adjacent sequences: A011668 A011669 A011670 this_sequence A011672 A011673 A011674
%Y A011671 Sequence in context: A104853 A079872 A011672 this_sequence A086483 A011667 A011759
%K A011671 nonn
%O A011671 0,1
%A A011671 njas

%I A086483
%S A086483 0,0,0,0,0,1,0,1,0,0,1,0,0,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,
%T A086483 0,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,
%U A086483 0,1,0,0,1,0,0,1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,1
%N A086483 Bit that is two places to left of least significant bit in binary expansion of n.
%e A086483 For n = 4, 5, 6, 7, 8 the binary expansions are 100, 101, 110, 111, 1000 and the values of a(n) are respectively 0, 1, 0, 1, 0.
%Y A086483 Cf. A038189.
%Y A086483 Adjacent sequences: A086480 A086481 A086482 this_sequence A086484 A086485 A086486
%Y A086483 Sequence in context: A079872 A011672 A011671 this_sequence A011667 A011759 A118952
%K A086483 nonn,easy
%O A086483 0,1
%A A086483 njas, Dec 22 2003
%E A086483 Corrected and extended by Douglas Gaut (dgaut(AT)ashland.edu), Apr 12 2004

%I A011667
%S A011667 0,0,0,0,0,1,0,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,1,0,0,
%T A011667 1,1,1,1,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0,
%U A011667 0,1,0,0,0,0,1,1,1,0,0,0,0,0,1,0,1,1,1,1,1,1,0,0,1,0,1
%N A011667 A binary m-sequence: expansion of reciprocal of x^6+x^5+x^3+x^2+1.
%D A011667 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011667 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011667 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011667 Adjacent sequences: A011664 A011665 A011666 this_sequence A011668 A011669 A011670
%Y A011667 Sequence in context: A011672 A011671 A086483 this_sequence A011759 A118952 A011668
%K A011667 nonn
%O A011667 0,1
%A A011667 njas

%I A011759
%S A011759 0,0,0,0,0,1,1,0,0,1,0,1,0
%N A011759 Barker sequence of length 13.
%D A011759 Eliahou, Shalom; Kervaire, Michel; Barker sequences and difference sets. Enseign. Math. (2) 38 (1992), no. 3-4, 345-382.
%D A011759 H. D. Lueke, Korrelationssignale, Springer 1992, p. 114.
%Y A011759 Cf. A011758, A091704.
%Y A011759 Adjacent sequences: A011756 A011757 A011758 this_sequence A011760 A011761 A011762
%Y A011759 Sequence in context: A011671 A086483 A011667 this_sequence A118952 A011668 A011670
%K A011759 nonn,fini,full
%O A011759 1,1
%A A011759 njas

%I A118952
%S A118952 0,0,0,0,0,1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0,0,1,1,
%T A118952 0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,1,0,0,1,1,0,1,0,
%U A118952 1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,1,0,0,0,1
%N A118952 Characteristic function of numbers that can be written as p+2^k, where p is prime and p less than 2^k (A118957).
%C A118952 0 <= a(n) <= 1, a(n) <= A109925(n);
%C A118952 a(A118956(n)) = 0, a(A118957(n)) = 1;
%C A118952 A118953(n) = a(A000040(n)).
%Y A118952 Adjacent sequences: A118949 A118950 A118951 this_sequence A118953 A118954 A118955
%Y A118952 Sequence in context: A086483 A011667 A011759 this_sequence A011668 A011670 A011666
%K A118952 nonn
%O A118952 1,1
%A A118952 Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), May 07 2006

%I A011668
%S A011668 0,0,0,0,0,1,1,0,1,1,1,0,0,1,1,0,0,0,1,1,1,0,1,0,1,1,1,
%T A011668 1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0,1,1,0,0,1,0,1,0,1,
%U A011668 0,0,1,0,0,1,1,1,1,0,0,0,0,0,1,1,0,1,1,1,0,0,1,1,0,0,0
%N A011668 A binary m-sequence: expansion of reciprocal of x^6+x^5+x^2+x+1.
%D A011668 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011668 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011668 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011668 Adjacent sequences: A011665 A011666 A011667 this_sequence A011669 A011670 A011671
%Y A011668 Sequence in context: A011667 A011759 A118952 this_sequence A011670 A011666 A011669
%K A011668 nonn
%O A011668 0,1
%A A011668 njas

%I A011670
%S A011670 0,0,0,0,0,1,1,1,0,0,0,0,1,0,0,1,0,0,0,1,1,0,1,1,0,0,1,
%T A011670 0,1,1,0,1,0,1,1,1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0,
%U A011670 0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0,0,1,0,0,1,0,0
%N A011670 A binary m-sequence: expansion of reciprocal of x^6+x^4+x^3+x+1.
%D A011670 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011670 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011670 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011670 Adjacent sequences: A011667 A011668 A011669 this_sequence A011671 A011672 A011673
%Y A011670 Sequence in context: A011759 A118952 A011668 this_sequence A011666 A011669 A023971
%K A011670 nonn
%O A011670 0,1
%A A011670 njas

%I A011666
%S A011666 0,0,0,0,0,1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0,1,1,0,1,0,0,
%T A011666 0,0,1,0,0,0,1,0,1,1,0,1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,1,
%U A011666 1,0,0,1,1,1,0,1,1,0,0,0,0,0,1,1,1,1,0,0,1,0,0,1,0,1,0
%N A011666 A binary m-sequence: expansion of reciprocal of x^6+x^5+x^4+x+1.
%D A011666 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011666 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011666 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011666 Adjacent sequences: A011663 A011664 A011665 this_sequence A011667 A011668 A011669
%Y A011666 Sequence in context: A118952 A011668 A011670 this_sequence A011669 A023971 A079260
%K A011666 nonn
%O A011666 0,1
%A A011666 njas

%I A011669
%S A011669 0,0,0,0,0,1,1,1,1,1,1,0,1,0,1,0,1,1,0,0,1,1,0,1,1,1,0,
%T A011669 1,1,0,1,0,0,1,0,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,1,0,1,0,
%U A011669 0,0,1,1,0,0,0,0,1,0,0,0,0,0,1,1,1,1,1,1,0,1,0,1,0,1,1
%N A011669 A binary m-sequence: expansion of reciprocal of x^6+x+1.
%D A011669 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011669 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011669 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%Y A011669 Adjacent sequences: A011666 A011667 A011668 this_sequence A011670 A011671 A011672
%Y A011669 Sequence in context: A011668 A011670 A011666 this_sequence A023971 A079260 A025457
%K A011669 nonn
%O A011669 0,1
%A A011669 njas

%I A023971
%S A023971 0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T A023971 0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%U A023971 1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A023971 First bit in fractional part of binary expansion of 4-th root of n.
%t A023971 Array[ Function[ n, RealDigits[ N[ Power[ n, 1/4 ], 10 ], 2 ]// (#[ [ 1, #[ [ 2 ] ]+1 ] ])& ], 110 ]
%Y A023971 Adjacent sequences: A023968 A023969 A023970 this_sequence A023972 A023973 A023974
%Y A023971 Sequence in context: A011670 A011666 A011669 this_sequence A079260 A025457 A093957
%K A023971 nonn,base
%O A023971 1,1
%A A023971 njas, Olivier Gerard (ogerard(AT)ext.jussieu.fr)

%I A079260
%S A079260 0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
%T A079260 0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
%U A079260 0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0
%N A079260 Characteristic function of primes of form 4n+1 (1 if n is prime of form 4n+1, 0 otherwise).
%C A079260 Let M(n) denote the n X n matrix m(i,j)=0 if n divides ij-1, m(i,j) = 1 otherwise then det(M(n))=-1 if and only if n =2 or if n is prime ==1 (mod 4).
%o A079260 (PARI) { a(n)=if(n%4==1,isprime(n)) }; vector(100,n,a(n))
%Y A079260 Cf. A002144.
%Y A079260 Adjacent sequences: A079257 A079258 A079259 this_sequence A079261 A079262 A079263
%Y A079260 Sequence in context: A011666 A011669 A023971 this_sequence A025457 A093957 A118685
%K A079260 nonn
%O A079260 1,1
%A A079260 Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 04 2003

%I A025457
%S A025457 0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,0,
%T A025457 0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0