A072872 - OEIS

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

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OFFSET

1,2

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

MATHEMATICA

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

PROG

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

CROSSREFS