A333336 a(n) is the smallest positive number k such that n divides 5^k + k.

1, 1, 1, 3, 5, 1, 6, 3, 2, 5, 6, 7, 12, 11, 20, 3, 4, 13, 18, 15, 37, 61, 22, 19, 25, 21, 2, 11, 6, 25, 30, 3, 61, 7, 15, 31, 4, 53, 14, 35, 18, 37, 42, 79, 20, 29, 25, 19, 6, 25, 7, 31, 52, 31, 10, 11, 79, 139, 58, 55, 60, 123, 38, 3, 125, 61, 52, 7, 49, 15

Offset

1,4

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.

Links

Table of n, a(n) for n=1..70.

Brazil National Olympiad, 2005, Problem 6

Formula

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

Prog

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

Crossrefs

Cf. A007736, A247248, A333334, A333335, A333341.

Sequence in context: A199616 A173973 A344076 * A061649 A237603 A073365

Adjacent sequences: A333333 A333334 A333335 * A333337 A333338 A333339

Keyword

nonn,easy

Author

Jinyuan Wang, Apr 14 2020

Status

approved