A135561 a(n) = 2^A135560(n) - 1.

3, 7, 1, 15, 1, 3, 1, 31, 1, 3, 1, 7, 1, 3, 1, 63, 1, 3, 1, 7, 1, 3, 1, 15, 1, 3, 1, 7, 1, 3, 1, 127, 1, 3, 1, 7, 1, 3, 1, 15, 1, 3, 1, 7, 1, 3, 1, 31, 1, 3, 1, 7, 1, 3, 1, 15, 1, 3, 1, 7, 1, 3, 1, 255, 1, 3, 1, 7, 1, 3, 1, 15, 1, 3, 1, 7, 1, 3, 1, 31, 1, 3, 1, 7, 1, 3, 1, 15, 1, 3, 1, 7, 1, 3, 1, 63, 1, 3

Offset

1,1

Links

R. Zumkeller, Table of n, a(n) for n = 1..10000

Formula

a(2^k) = 2^(k+2) - 1; a(2^k + 2^(k-1)) = 2^k - 1. - Reinhard Zumkeller, Mar 02 2008

Mathematica

f[n_] := 1 + IntegerExponent[n, 2] + Sum[(-1)^(n - k - 1)*Binomial[n - 1, k]* Sum[Binomial[k, 2^j - 1], {j, 0, k}], {k, 0, n - 1}]; Table[2^f[k] - 1, {k, 1, 20}] (* G. C. Greubel, Oct 17 2016 *)

Prog

(Python)
def A135561(n): return (1<<(m:=(~n & n-1)).bit_length()+int(m==n-1)+1)-1 # Chai Wah Wu, Jul 06 2022

Crossrefs

Cf. A007814, A036987, A091090, A135534, A135560.

Sequence in context: A191335 A338366 A124138 * A196231 A210037 A210197

Adjacent sequences: A135558 A135559 A135560 * A135562 A135563 A135564

Keyword

nonn,easy

Author

N. J. A. Sloane, Mar 01 2008

Extensions

More terms from Reinhard Zumkeller, Mar 02 2008

Status

approved