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A089263 First differences of A080791. 1
0, 0, 1, -1, 2, -1, 0, -1, 3, -1, 0, -1, 1, -1, 0, -1, 4, -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, 1, -1, 0, -1, 2, -1, 0, -1, 1, -1, 0, -1, 6, -1, 0, -1, 1, -1, 0, -1, 2, -1, 0, -1, 1, -1 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
Number of trailing zeros in the binary representation of n, minus one if n is not a power of two.
a(0) = 0 by convention. - Antti Karttunen, Sep 27 2018
LINKS
FORMULA
a(0)=0, a(2n) = a(n) + 1, a(2n+1) = -1 + [n==0].
a(n) = A007814(n) + A036987(n-1) - 1.
G.f.: sum(k>=0, t^2/(1+t), t=x^2^k).
a(n) = A080791(n+1) - A080791(n). - Antti Karttunen, Sep 27 2018
PROG
(PARI) a(n)=if(!n, n, (valuation(n, 2)+(2^valuation(n, 2)==n)-1)); \\ Check for n=0 added by Antti Karttunen, Sep 27 2018
(PARI) a(n)=if(n<1, 0, if(n%2==0, a(n/2)+1, -1+(((n-1)/2)==0)))
CROSSREFS
Sequence in context: A052249 A030528 A077227 * A348951 A369815 A156135
KEYWORD
sign,easy
AUTHOR
Ralf Stephan, Oct 30 2003
EXTENSIONS
Definition corrected (A023416 replaced with A080791) by Antti Karttunen, Sep 27 2018
STATUS
approved

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Last modified March 28 10:31 EDT 2024. Contains 371240 sequences. (Running on oeis4.)