login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A135366
a(n) is the smallest nonnegative k such that n divides 2^k + k.
2
0, 2, 1, 4, 4, 2, 6, 8, 7, 4, 3, 8, 12, 6, 7, 16, 16, 14, 18, 4, 19, 8, 22, 8, 33, 12, 7, 40, 11, 26, 23, 32, 8, 16, 6, 32, 5, 18, 37, 24, 40, 38, 42, 8, 7, 22, 10, 32, 61, 84, 38, 12, 35, 32, 46, 40, 32, 28, 24, 44
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
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
Sequence in context: A261070 A249140 A113421 * A247248 A192017 A180566
KEYWORD
nonn
AUTHOR
John L. Drost, Feb 16 2008
EXTENSIONS
Corrected by Harvey P. Dale, Jun 01 2013
STATUS
approved