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 A088705 First differences of A000120. One minus exponent of 2 in n. 10
 0, 1, 0, 1, -1, 1, 0, 1, -2, 1, 0, 1, -1, 1, 0, 1, -3, 1, 0, 1, -1, 1, 0, 1, -2, 1, 0, 1, -1, 1, 0, 1, -4, 1, 0, 1, -1, 1, 0, 1, -2, 1, 0, 1, -1, 1, 0, 1, -3, 1, 0, 1, -1, 1, 0, 1, -2, 1, 0, 1, -1, 1, 0, 1, -5, 1, 0, 1, -1, 1, 0, 1, -2, 1, 0, 1, -1, 1, 0, 1, -3, 1, 0, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,9 COMMENTS The number of 1's in the binary expansion of n+1 minus the number of 1's in the binary expansion of n. For n > 0: a(n) = A000120(n) - A000120(n-1) = 1 - A007814(n). Multiplicative with a(2^e) = 1-e, a(p^e) = 1 otherwise. [David W. Wilson, Jun 12 2005] LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..10000 Yann Bugeaud and Guo-Niu Han, A combinatorial proof of the non-vanishing of Hankel determinants of the Thue-Morse sequence, Electronic Journal of Combinatorics 21(3) (2014), #P3.26. See F(z) in (1.1). - N. J. A. Sloane, Aug 31 2014 R. Stephan, Some divide-and-conquer sequences ... R. Stephan, Table of generating functions FORMULA G.f.: sum(k>=0, t/(1+t), t=x^2^k). a(0)=0, a(2*n) = a(n) - 1, a(2*n+1) = 1. Let T(x) be the g.f., then T(x)-T(x^2)=x/(1+x). [Joerg Arndt, May 11 2010] MAPLE add(x^(2^k)/(1+x^(2^k)), k=0..20); series(%, x, 1001); seriestolist(%); # To get up to a million terms, from N. J. A. Sloane, Aug 31 2014 MATHEMATICA a[n_] := If[n<1, 0, If[Mod[n, 2] == 0, a[n/2] - 1, 1]]; Array[a, 60, 0] (* Amiram Eldar, Nov 26 2018 *) PROG (PARI) a(n)=if(n<1, 0, if(n%2==0, a(n/2)-1, 1)) (PARI) a(n)=if(n<1, 0, 1-valuation(n, 2)) (Haskell) a088705 n = a088705_list !! n a088705_list = 0 : zipWith (-) (tail a000120_list) a000120_list -- Reinhard Zumkeller, Dec 11 2011 CROSSREFS Cf. A079559. Sequence in context: A016353 A016398 A024359 * A065712 A153172 A242498 Adjacent sequences:  A088702 A088703 A088704 * A088706 A088707 A088708 KEYWORD sign,easy,mult AUTHOR Ralf Stephan, Oct 10 2003 STATUS approved

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Last modified January 17 14:12 EST 2019. Contains 319225 sequences. (Running on oeis4.)