A333334 a(n) is the smallest positive number k such that n divides 3^k + k.

1, 1, 3, 1, 3, 3, 6, 5, 9, 3, 2, 9, 10, 15, 3, 13, 4, 9, 18, 17, 6, 29, 22, 21, 23, 17, 27, 25, 28, 3, 5, 13, 57, 23, 6, 9, 36, 23, 12, 37, 40, 15, 17, 29, 63, 63, 35, 45, 6, 23, 27, 17, 19, 27, 57, 109, 18, 31, 10, 57, 52, 5, 90, 45, 17, 57, 66, 65, 63, 23, 70

Offset

1,3

Comments

For any positive integer n, if k = a(n) + n*m*A007734(n) and m >= 0 then 3^k + k is divisible by n.

Links

Seiichi Manyama, Table of n, a(n) for n = 1..5000

Brazil National Olympiad, 2005, Problem 6

Formula

a(3^m) = 3^m for m >= 0.

a(p) <= p - 1 if p is a prime greater than 3.

Mathematica

a[n_] := Module[{k = 1}, While[!Divisible[3^k + k, n], k++]; k]; Array[a, 100] (* Amiram Eldar, Mar 16 2020 *)

Prog

(PARI) a(n) = for(k=1, oo, if(Mod(3, n)^k==-k, return(k)));

Crossrefs

Cf. A007734, A247248, A333335, A333336, A333339.

Sequence in context: A259286 A087891 A005885 * A205145 A061892 A038573

Adjacent sequences: A333331 A333332 A333333 * A333335 A333336 A333337

Keyword

nonn,easy

Author

Jinyuan Wang, Mar 15 2020

Status

approved