Search: id:A007088
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%I A007088 M4679
%S A007088 0,1,10,11,100,101,110,111,1000,1001,1010,1011,1100,1101,1110,1111,10000,
%T A007088 10001,10010,10011,10100,10101,10110,10111,11000,11001,11010,11011,11100,
%U A007088 11101,11110,11111,100000,100001,100010,100011,100100,100101,100110,100111
%N A007088 Numbers written in base 2.
%C A007088 Or, numbers that are sums of distinct powers of 10.
%C A007088 Or, decimal numbers that only mention 0 and 1.
%C A007088 Complement of A136399; A064770(a(n)) = a(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Dec 30 2007
%C A007088 a(A000290(n)) = A001737(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Apr 25 2009]
%C A007088 Contribution from Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jun 25 
               2009: (Start)
%C A007088 Nonnegative integers with no decimal digit > 1.
%C A007088 Thus nonnegative integers n in base 10 such that kn can be calculated 
               by normal addition (i.e., n + n + ... + n, with k n's (but not necessarily 
               k + k + ... + k, with n k's)) or multiplication without requiring 
               any carry operations for 0 <= k <= 9. (End)
%D A007088 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A007088 Franklin T. Adams-Watters, <a href="b007088.txt">Table of n, a(n) for 
               n = 0..8192</a>
%H A007088 <a href="Sindx_Bi.html#binary">Index entries for sequences related to 
               binary expansion of n</a>
%F A007088 a(n)=Sum{d(i)*10^i: i=0, 1, ..., m}, where Sum{d(i)*2^i: i=0, 1, ..., 
               m} is the base 2 representation of n.
%F A007088 a(n)=(1/2)*sum(i => 0, (1-(-1)^floor(n/2^i))*10^i). - Benoit Cloitre 
               (benoit7848c(AT)orange.fr), Nov 20 2001
%F A007088 a(n) = A097256(n)/9.
%F A007088 a(2n) = 10*a(n), a(2n+1) = a(2n)+1.
%F A007088 G.f. 1/(1-x) * Sum_{k>=0} 10^k * x^{2^k}/(1+x^{2^k}) - for sequence as 
               decimal integers. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), 
               Jun 16 2006
%e A007088 a(6)=110 because (1/2)*((1-(-1)^6)*10^0+(1-(-1)^3)*10^1+(1-(-1)^1)*10^2) 
               = 10+100
%p A007088 A007088 := proc(n) local dgs ; dgs := convert(n,base,2) ; add( op(i,dgs)*10^(i-1),
               i=1..nops(dgs)) ; end: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Aug 11 2009]
%t A007088 Table[ FromDigits[ IntegerDigits[n, 2]], {n, 0, 39}]
%o A007088 (PARI) a(n)=subst(Pol(binary(n)),x,10)
%o A007088 (PARI) a(n)=if(n<=0,0,n%2+10*a(n\2))
%Y A007088 The basic sequences concerning the binary expansion of n are this one, 
               A000788, A000069, A001969, A023416, A059015, A000120.
%Y A007088 Cf. A000042, A007089, A007090, A007091, A007092, A007093, A007094 & A007095.
%Y A007088 Cf. A000695, A005836, A033042-A033052.
%Y A007088 A159918. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Apr 25 2009]
%Y A007088 Sequence in context: A136830 A153069 A081551 this_sequence A115848 A136814 
               A136809
%Y A007088 Adjacent sequences: A007085 A007086 A007087 this_sequence A007089 A007090 
               A007091
%K A007088 nonn,nice,easy
%O A007088 0,3
%A A007088 N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)

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