A255308 Number of times log_2 can be applied to n until the result is not a power of 2. Here log_2 means the base-2 logarithm.

0, 1, 2, 0, 3, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 4, 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
• mult

Comments

Multiplicative because only powers of two have a nonzero value. - Andrew Howroyd, Jul 27 2018

Links

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

Crossrefs

Cf. A209229, A255309.

One less than A293668.

Programs

PARI

a(n) = if(n < 1, 0, my(e=valuation(n, 2)); if(n == 2^e, 1 + a(e), 0)) \\ Andrew Howroyd, Jul 27 2018

Formula

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

Extensions

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