This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A317587 #35 Aug 11 2018 15:35:25
%S A317587 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 A317587 29,29,29,31,31,37,37,37,36,37,37,40,41,41,41,43,43,47,47,47,47,53,53,
%U A317587 53,53,53,53,59,59,59,59,59,59,61,61,67,67,67,67,67,67,71,71,71,71
%N A317587 a(n) is the smallest number m > n such that Sum_{k=1..n-1} k^(m-1) == n-1 (mod m).
%C A317587 a(n) <= A317357(n-1).
%C A317587 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 A317587 The smallest odd composite term is a(201) = 207. Are there any more? - _Michel Marcus_, Jul 02 2018
%C A317587 Conjecture: If p is a prime, then odd a(p) is the next prime after p. - _Thomas Ordowski_, Aug 06 2018
%t A317587 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 A317587 (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 A317587 Cf. A065091, A151800, A317357.
%K A317587 nonn
%O A317587 2,1
%A A317587 _Thomas Ordowski_, Aug 01 2018
%E A317587 More terms from _Michel Marcus_, Aug 01 2018