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

2,1

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

Links

Table of n, a(n) for n=2..70.

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 *)

Prog

(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

Crossrefs

Cf. A065091, A151800, A317357.

Sequence in context: A205560 A195939 A331859 * A235647 A010616 A296485

Adjacent sequences: A317584 A317585 A317586 * A317588 A317589 A317590

Keyword

nonn

Author

Thomas Ordowski, Aug 01 2018

Extensions

More terms from Michel Marcus, Aug 01 2018

Status

approved