A317587 a(n) is the smallest number m > n such that Sum_{k=1..n-1} k^(m-1) == n-1 (mod m).

3, 5, 5, 6, 7, 11, 11, 11, 11, 13, 13, 16, 17, 17, 17, 19, 19, 23, 23, 23, 23, 29, 29, 29, 29, 29, 29, 31, 31, 37, 37, 37, 36, 37, 37, 40, 41, 41, 41, 43, 43, 47, 47, 47, 47, 53, 53, 53, 53, 53, 53, 59, 59, 59, 59, 59, 59, 61, 61, 67, 67, 67, 67, 67, 67, 71, 71, 71, 71

Offset: 2

Author

Thomas Ordowski, Aug 01 2018

Keywords

• nonn

Comments

a(n) <= A317357(n-1).

a(n) <= A151800(n), where a(n) < A151800(n) for n = 5, 13, 34, 37, ... with composite terms a(n) = 6, 16, 36, 40, ...

The smallest odd composite term is a(201) = 207. Are there any more? - Michel Marcus, Jul 02 2018

Conjecture: If p is a prime, then odd a(p) is the next prime after p. - Thomas Ordowski, Aug 06 2018

Crossrefs

Cf. A065091, A151800, A317357.

Programs

Mathematica

Array[Block[{m = # + 1}, While[Mod[Sum[k^(m - 1), {k, # - 1}], m] != # - 1, m++]; m] &, 69, 2] (* Michael De Vlieger, Aug 02 2018 *)

PARI

a(n) = for(m=n+1, oo, if (sum(k=1, n-1, Mod(k, m)^(m-1)) == Mod(n-1, m), return (m)); ); \\ Michel Marcus, Aug 01 2018

Extensions

More terms from Michel Marcus, Aug 01 2018