A333334 - OEIS

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

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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