A255309 Number of times log_2 can be applied to n until the result is either 1 or not a power of 2. Here log_2 means the base-2 logarithm.

0, 0, 1, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

Offset: 0

Author

Paul Boddington, Feb 20 2015

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A000079 (2^n), A007814 (2-adic valuation of n), A209229, A255308.

Programs

PARI

nbi(n) = {my(nb = 0); if ((ispower(n, ,&m) && (m==2)) || (n==2), return(nbi(valuation(n, 2))+1);); nb;}
a(n) = { my(nb = 0); if ((ispower(n, ,&m) && (m==2)) || (n==2), return(nbi(valuation(n, 2))+1);); nb;} \\ Michel Marcus, Mar 11 2015; corrected Jun 13 2022

PARI

A255309(n) = { my(k=0); while((n>1)&&!bitand(n,n-1),n = valuation(n,2); k++); (k); }; \\ Antti Karttunen, Sep 30 2018

Formula

a(n) = 1 + a(log_2(n)) if n is a power of 2 except 1, 0 otherwise.

Extensions

Extended up to a(128) by Antti Karttunen, Sep 30 2018