OFFSET
1,2
COMMENTS
a(2^m) = 2^m for m > 0. If p is an odd prime then by Fermat, a(p) <= p-1. 25 is the smallest n with a(n) > n.
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
International Mathematical Olympiad, Problem N7, IMO-2006, p. 63.
EXAMPLE
a(9)=7 since 2^7 + 7 = 9*15 and 2^k + k is not divisible by 9 for 0 <= k < 7.
MATHEMATICA
sk[n_]:=Module[{k=0}, While[!Divisible[2^k+k, n], k++]; k]; Array[sk, 60] (* Harvey P. Dale, Jun 01 2013 *)
PROG
(PARI) a(n) = for(m=0, oo, if(Mod(2, n)^m==-m, return(m))); \\ Jinyuan Wang, Mar 15 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
John L. Drost, Feb 16 2008
EXTENSIONS
Corrected by Harvey P. Dale, Jun 01 2013
STATUS
approved