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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

Antti Karttunen, Table of n, a(n) for n = 0..65537

Index entries for sequences related to binary expansion of n

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

Cf. A080791, A088705.

Sequence in context: A052249 A030528 A077227 * A156135 A047265 A185962

Adjacent sequences:  A089260 A089261 A089262 * A089264 A089265 A089266

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 October 21 08:42 EDT 2018. Contains 316405 sequences. (Running on oeis4.)