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

1,2

Links

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

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

Maple

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

Prog

(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

Crossrefs

Cf. A135416, A007814, A036987.

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

One less than A135560.

Sequence in context: A219202 A341980 A218031 * A194663 A135685 A349447

Adjacent sequences: A135520 A135521 A135522 * A135524 A135525 A135526

Keyword

nonn,easy

Author

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

Status

approved