login
A333336
a(n) is the smallest positive number k such that n divides 5^k + k.
3
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
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
KEYWORD
nonn,easy
AUTHOR
Jinyuan Wang, Apr 14 2020
STATUS
approved