A135359 a(n) is the smallest nonnegative number k such that n divides 2^k-k.

0, 2, 4, 4, 3, 4, 11, 8, 5, 14, 7, 4, 10, 16, 16, 16, 30, 16, 30, 16, 11, 58, 75, 16, 34, 10, 5, 16, 6, 16, 8, 32, 58, 30, 16, 16, 58, 30, 10, 16, 33, 16, 54, 92, 16, 118, 224, 16, 36, 34, 59, 16, 36, 34, 63, 16, 130, 6, 64, 16, 43, 8, 16, 64, 16, 58, 210, 84, 118, 16, 43, 16, 32

Offset: 1

Author

John L. Drost, Feb 16 2008

Keywords

• nonn

Examples

			a(7)=11, since 2^11-11= 3*7*97 and 2^k-k is not divisible by 7 for 0<=k<11.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

See A072872 for another version.

Programs

Magma

S:=[0];
k:=1;
for n in [2..80] do
  while not IsZero((2^k-k) mod n) do
       k:=k+1;
  end while;
  Append(~S, k);
  k:=1;
end for;
S; // Bruno Berselli, Aug 18 2013

Mathematica

b[n_] := Module[{k = 0}, While[! Divisible[2^k - k, n], k++]; k]; Array[b, 25] (* G. C. Greubel, Oct 11 2016 *)

PARI

a(n) = {my(k = 0); while ((2^k-k) % n, k++); k;} \\ Michel Marcus, Aug 18 2013

Extensions

Edited by N. J. A. Sloane, May 27 2010