|
%I #35 Aug 11 2018 15:35:25
%S 3,5,5,6,7,11,11,11,11,13,13,16,17,17,17,19,19,23,23,23,23,29,29,29,
%T 29,29,29,31,31,37,37,37,36,37,37,40,41,41,41,43,43,47,47,47,47,53,53,
%U 53,53,53,53,59,59,59,59,59,59,61,61,67,67,67,67,67,67,71,71,71,71
%N a(n) is the smallest number m > n such that Sum_{k=1..n-1} k^(m-1) == n-1 (mod m).
%C a(n) <= A317357(n-1).
%C a(n) <= A151800(n), where a(n) < A151800(n) for n = 5, 13, 34, 37, ... with composite terms a(n) = 6, 16, 36, 40, ...
%C The smallest odd composite term is a(201) = 207. Are there any more? - _Michel Marcus_, Jul 02 2018
%C Conjecture: If p is a prime, then odd a(p) is the next prime after p. - _Thomas Ordowski_, Aug 06 2018
%t Array[Block[{m = # + 1}, While[Mod[Sum[k^(m - 1), {k, # - 1}], m] != # - 1, m++]; m] &, 69, 2] (* _Michael De Vlieger_, Aug 02 2018 *)
%o (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
%Y Cf. A065091, A151800, A317357.
%K nonn
%O 2,1
%A _Thomas Ordowski_, Aug 01 2018
%E More terms from _Michel Marcus_, Aug 01 2018
|
