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A088705
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First differences of A000120. One minus exponent of 2 in n.
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5
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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; internal format)
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OFFSET
| 0,9
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COMMENTS
| 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]
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LINKS
| R. Stephan, Some divide-and-conquer sequences ...
R. Stephan, Table of generating functions
Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
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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]
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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
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CROSSREFS
| Cf. A079559.
Sequence in context: A016353 A016398 A024359 * A065712 A153172 A016194
Adjacent sequences: A088702 A088703 A088704 * A088706 A088707 A088708
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KEYWORD
| sign,easy,mult
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AUTHOR
| Ralf Stephan (ralf(AT)ark.in-berlin.de), Oct 10 2003
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