A072872 a(n) is the smallest positive number k such that n divides 2^k - k.

1, 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

Benoit Cloitre, Jul 28 2002

Keywords

• nonn
• easy

Comments

If n is a power of 2, a(n) = n. Conjecture : if n > 47, a(n) < prime(n).

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

See A135359 for another version.

Cf. A247248.

Programs

Mathematica

dvkn[n_]:=Module[{k=1},While[!Divisible[2^k-k,n],k++];k]; Array[dvkn,80] (* Harvey P. Dale, Dec 23 2011 *)

PARI

a(n) = for(k=1, oo, if(Mod(2, n)^k==k, return(k))); \\ Jinyuan Wang, Mar 15 2020

Extensions

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