A333341 a(n) is the smallest positive number k such that n divides 5^k - k.

1, 1, 4, 1, 5, 5, 16, 5, 4, 5, 9, 5, 5, 17, 5, 5, 11, 11, 16, 5, 16, 9, 2, 5, 25, 5, 4, 17, 74, 5, 56, 21, 16, 11, 100, 29, 13, 101, 5, 5, 43, 17, 27, 9, 40, 61, 8, 5, 32, 25, 11, 5, 28, 29, 45, 61, 16, 149, 21, 5, 3, 63, 58, 53, 5, 47, 75, 133, 4, 145, 76, 29

Offset: 1

Author

Jinyuan Wang, Apr 14 2020

Keywords

• nonn

Comments

For any positive integer n, if k = a(n) + n*m*A007736(n) and m >= 0 then 5^k - k is divisible by n.

Crossrefs

Cf. A007736, A072872, A333336, A333339, A333340.

Programs

PARI

a(n) = for(k=1, oo, if(Mod(5, n)^k==k, return(k)));

Formula

a(5^m) = 5^m for m >= 0.