A218362 - OEIS

%I #12 Oct 24 2022 07:46:09

%S 1,4,27,16,151,7,701,17,81,11,104281,13,599,197,31,64,3044803,199,

%T 109912203092239643840221,176,18927,23,277,119,101,131,243,29,59,61,

%U 243270318891483838103593381595151809701,97,67,12179212,71,37,149,108301,79,41,10654507

%N Minimal order of degree-n irreducible polynomials over GF(19).

%C a(n) < 19^n.

%H Max Alekseyev, <a href="/A218362/b218362.txt">Table of n, a(n) for n = 1..238</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/IrreduciblePolynomial.html">Irreducible Polynomial</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PolynomialOrder.html">Polynomial Order</a>

%F 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 a(n) = A218339(n,1) = A213224(n,8).

%p with(numtheory):

%p M:= proc(n) M(n):= divisors(19^n-1) minus U(n-1) end:

%p U:= proc(n) U(n):= `if`(n=0, {}, M(n) union U(n-1)) end:

%p a:= n-> min(M(n)[]):

%p seq(a(n), n=1..28);

%t M[n_] := M[n] = Divisors[19^n - 1]~Complement~U[n - 1];

%t U[n_] := U[n] = If[n == 0, {}, M[n]~Union~U[n - 1]];

%t a[n_] := Min[M[n]];

%t Table[a[n], {n, 1, 41}] (* _Jean-François Alcover_, Oct 24 2022, after _Alois P. Heinz_ *)

%Y Cf. A213224, A218339.

%K nonn

%O 1,2

%A _Alois P. Heinz_, Oct 27 2012