A089263 First differences of A080791.

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

Offset: 0

Author

Ralf Stephan, Oct 30 2003

Keywords

• sign
• easy

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

Crossrefs

Cf. A080791, A088705.

Programs

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)))

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

Extensions

Definition corrected (A023416 replaced with A080791) by Antti Karttunen, Sep 27 2018