A135534 a(1) = 1; for n>=1, a(2n) = A135561(n), a(2n+1) = 0.

1, 3, 0, 7, 0, 1, 0, 15, 0, 1, 0, 3, 0, 1, 0, 31, 0, 1, 0, 3, 0, 1, 0, 7, 0, 1, 0, 3, 0, 1, 0, 63, 0, 1, 0, 3, 0, 1, 0, 7, 0, 1, 0, 3, 0, 1, 0, 15, 0, 1, 0, 3, 0, 1, 0, 7, 0, 1, 0, 3, 0, 1, 0, 127, 0, 1, 0, 3, 0, 1, 0, 7, 0, 1, 0, 3, 0, 1, 0, 15, 0, 1, 0, 3, 0, 1, 0, 7, 0, 1, 0, 3, 0, 1, 0, 31, 0, 1, 0, 3, 0, 1

Offset: 1

Author

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

Keywords

• nonn

Links

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

Crossrefs

Cf. A135416.

This is Guy Steele's sequence GS(6, 1) (see A135416).

Programs

Maple

GS(6,1,200); [see A135416].

PARI

A135560(n) = { my(t=valuation(n, 2)); (t + (n==2^t) + 1); }; \\ From A135560
A135534(n) = if(1==n,1,if((n%2),0,((2^(A135560(n/2)))-1))); \\ Antti Karttunen, Sep 27 2018

Python

def A135534(n): return 1 if n == 1 else 0 if n&1 else (1<<(m:=(~(k:=n>>1) & k-1)).bit_length()+int(m==k-1)+1)-1 # Chai Wah Wu, Jul 06 2022