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.
2, 31, 757, 65537, 19531, 3154757, 2767631689, 9857737155463, 926510094425921, 440334654777631, 50544702849929377, 3335672988472972523, 846041103974872866961, 459715689149916492091, 92978587355640205970336221, 78919881726271091143763623681, 26552618219228090162977481, 1338029376807245057016053427001, 11951068054199383402102234839038071
Offset: 1
Crossrefs
Inspired by A333245.
Programs
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Maple
f:= proc(n) local k, pmin, p; pmin:= infinity; for k from n while k^n < pmin do for p in numtheory:-factorset(n^k-1) do if p < pmin and p > k^n then pmin:= p fi od od; pmin end proc: f(1):= 2: seq(f(n),n=1..18); # Robert Israel, Mar 17 2020
Extensions
More terms from Robert Israel, Mar 17 2020