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A333349 a(n) is the least prime p such that n <= ord(n, p)^n < p, where ord(n, p) is the multiplicative order of n modulo p, or 1, if there is no such p.

%I A333349 #30 Mar 17 2020 14:37:57
%S A333349 2,31,757,65537,19531,3154757,2767631689,9857737155463,
%T A333349 926510094425921,440334654777631,50544702849929377,
%U A333349 3335672988472972523,846041103974872866961,459715689149916492091,92978587355640205970336221,78919881726271091143763623681,26552618219228090162977481,1338029376807245057016053427001,11951068054199383402102234839038071
%N A333349 a(n) is the least prime p such that n <= ord(n, p)^n < p, where ord(n, p) is the multiplicative order of n modulo p, or 1, if there is no such p.
%p A333349 f:= proc(n) local k, pmin, p;
%p A333349   pmin:= infinity;
%p A333349   for k from n while k^n < pmin do
%p A333349     for p in numtheory:-factorset(n^k-1) do
%p A333349       if p < pmin and p > k^n then pmin:= p fi
%p A333349     od
%p A333349   od;
%p A333349   pmin
%p A333349 end proc:
%p A333349 f(1):= 2:
%p A333349 seq(f(n),n=1..18); # _Robert Israel_, Mar 17 2020
%Y A333349 Inspired by A333245.
%K A333349 nonn,hard
%O A333349 1,1
%A A333349 _Peter Luschny_, Mar 17 2020
%E A333349 More terms from _Robert Israel_, Mar 17 2020