A135523 a(n) = A007814(n) + A209229(n).

1, 2, 0, 3, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 6, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 7, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 5, 0, 1, 0, 2, 0, 1, 0, 3, 0

Offset: 1

Author

N. J. A. Sloane, based on a message from Guy Steele and Don Knuth, Mar 01 2008

Keywords

• nonn
• easy

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A135416, A007814, A036987.

This is Guy Steele's sequence GS(4, 1) (see A135416).

One less than A135560.

Programs

Maple

GS(4,1,200); [see A135416].

PARI

A135523(n) = (valuation(n,2)+(n && !bitand(n,n-1))); \\ Antti Karttunen, Sep 27 2018

Python

def A135523(n): return (~n& n-1).bit_length()+int(not(n&-n)^n) # Chai Wah Wu, Jul 08 2022

Formula

G.f.: x + Sum_{k>=1} x^(2^k)*(1 + 1/(1 - x^(2^k))). - Ilya Gutkovskiy, Mar 30 2017

a(n) = A135560(n) - 1. Antti Karttunen, Sep 27 2018