Search: id:A001951
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%I A001951 M0955 N0356
%S A001951 0,1,2,4,5,7,8,9,11,12,14,15,16,18,19,21,22,24,25,26,28,29,31,32,33,35,
%T A001951 36,38,39,41,42,43,45,46,48,49,50,52,53,55,56,57,59,60,62,63,65,66,67,
%U A001951 69,70,72,73,74,76,77,79,80,82,83,84,86,87,89,90,91,93,94,96,97,98,100
%N A001951 A Beatty sequence: a(n) = floor[n*sqrt 2].
%C A001951 Earliest monotonic sequence >0 satisfying the condition : "a(n)+2n is 
               not in the sequence" - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Mar 25 2004
%C A001951 Also the integer part of the hypotenuse of isosceles right triangles. 
               The real part of these numbers is irrational. For proof see Jones 
               and Jones.
%C A001951 First differences are 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, ..(A006337) 
               . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), May 29 2006
%D A001951 L. Carlitz, R. Scoville and V. E. Hoggatt, Jr., Pellian representatives, 
               Fib. Quart., 10 (1972), 449-488.
%D A001951 I. G. Connell, A generalization of Wythoff's game, Canad. Math. Bull., 
               2 (1959), 181-190.
%D A001951 A. S. Fraenkel, How to beat your Wythoff games' opponent on three fronts, 
               Amer. Math. Monthly, 89 (1982), 353-361 (the case a=2).
%D A001951 R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, 
               Reading, MA, 1990, p. 77.
%D A001951 Gareth A. Jones and J. Mary Jones, Elementary Number Theory, Springer, 
               1998; pp. 221-222.
%D A001951 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001951 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A001951 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               BeattySequence.html">Link to a section of The World of Mathematics.</
               a>
%H A001951 <a href="Sindx_Be.html#Beatty">Index entries for sequences related to 
               Beatty sequences</a>
%o A001951 (PARI) f(n) = for(j=1,n,print1(floor(sqrt(2*j^2))","))
%Y A001951 Complement of A001952. Equals A001952(n)-2*n.
%Y A001951 A003151(n) - n.
%Y A001951 Cf. A022342.
%Y A001951 Cf. A026250.
%Y A001951 A bisection of A094077.
%Y A001951 Sequence in context: A014132 A047381 A097506 this_sequence A039046 A026451 
               A050106
%Y A001951 Adjacent sequences: A001948 A001949 A001950 this_sequence A001952 A001953 
               A001954
%K A001951 nonn,nice,easy
%O A001951 0,3
%A A001951 N. J. A. Sloane (njas(AT)research.att.com).
%E A001951 More terms from David W. Wilson (davidwwilson(AT)comcast.net), Sep 20 
               2000

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