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 A218362 #13 Feb 16 2025 08:33:18
%S A218362 1,4,27,16,151,7,701,17,81,11,104281,13,599,197,31,64,3044803,199,
%T A218362 109912203092239643840221,176,18927,23,277,119,101,131,243,29,59,61,
%U A218362 243270318891483838103593381595151809701,97,67,12179212,71,37,149,108301,79,41,10654507
%N A218362 Minimal order of degree-n irreducible polynomials over GF(19).
%C A218362 a(n) < 19^n.
%H A218362 Max Alekseyev, <a href="/A218362/b218362.txt">Table of n, a(n) for n = 1..238</a>
%H A218362 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IrreduciblePolynomial.html">Irreducible Polynomial</a>
%H A218362 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PolynomialOrder.html">Polynomial Order</a>
%F A218362 a(n) = min(M(n)) with M(n) = {d : d|(19^n-1)} \ U(n-1) and U(n) = M(n) union U(n-1) for n>0, U(0) = {}.
%F A218362 a(n) = A218339(n,1) = A213224(n,8).
%p A218362 with(numtheory):
%p A218362 M:= proc(n) M(n):= divisors(19^n-1) minus U(n-1) end:
%p A218362 U:= proc(n) U(n):= `if`(n=0, {}, M(n) union U(n-1)) end:
%p A218362 a:= n-> min(M(n)[]):
%p A218362 seq(a(n), n=1..28);
%t A218362 M[n_] := M[n] = Divisors[19^n - 1]~Complement~U[n - 1];
%t A218362 U[n_] := U[n] = If[n == 0, {}, M[n]~Union~U[n - 1]];
%t A218362 a[n_] := Min[M[n]];
%t A218362 Table[a[n], {n, 1, 41}] (* _Jean-François Alcover_, Oct 24 2022, after _Alois P. Heinz_ *)
%Y A218362 Cf. A213224, A218339.
%K A218362 nonn
%O A218362 1,2
%A A218362 _Alois P. Heinz_, Oct 27 2012