A333335 a(n) is the smallest positive number k such that n divides 4^k + k.

1, 2, 2, 4, 1, 2, 5, 8, 2, 4, 10, 8, 4, 6, 11, 16, 13, 2, 12, 4, 5, 10, 22, 8, 21, 4, 11, 48, 28, 14, 30, 32, 17, 16, 31, 20, 7, 12, 29, 24, 40, 26, 42, 68, 11, 22, 44, 32, 5, 44, 86, 4, 52, 38, 51, 48, 59, 28, 50, 44, 60, 30, 47, 64, 4, 68, 3, 16, 158, 94, 70

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Brazil National Olympiad, 2005, Problem 6

Formula

a(4^m) = 4^m for m >= 0.

Maple

f:= proc(n) local k;
  for k from 1 do if 4 &^ k + k mod n = 0 then return k fi od
end proc:
map(f, [$1..100]); # Robert Israel, Feb 05 2026

Mathematica

Table[k = 0; Until[Divisible[4^k + k, n], k++]; k, {n, 71}] (* Michael De Vlieger, Feb 05 2026 *)

Prog

(PARI) a(n) = for(k=1, oo, if(Mod(4, n)^k==-k, return(k)));

Crossrefs

Cf. A247248, A333334, A333336, A333340.

Sequence in context: A317836 A214740 A064848 * A394661 A212791 A175001

Adjacent sequences: A333332 A333333 A333334 * A333336 A333337 A333338

Keyword

nonn,easy

Author

Jinyuan Wang, Apr 14 2020

Status

approved