A218362 Minimal order of degree-n irreducible polynomials over GF(19).

1, 4, 27, 16, 151, 7, 701, 17, 81, 11, 104281, 13, 599, 197, 31, 64, 3044803, 199, 109912203092239643840221, 176, 18927, 23, 277, 119, 101, 131, 243, 29, 59, 61, 243270318891483838103593381595151809701, 97, 67, 12179212, 71, 37, 149, 108301, 79, 41, 10654507

Offset

1,2

Comments

a(n) < 19^n.

Links

Max Alekseyev, Table of n, a(n) for n = 1..238

Eric Weisstein's World of Mathematics, Irreducible Polynomial

Eric Weisstein's World of Mathematics, Polynomial Order

Formula

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) = {}.

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

Maple

with(numtheory):
M:= proc(n) M(n):= divisors(19^n-1) minus U(n-1) end:
U:= proc(n) U(n):= `if`(n=0, {}, M(n) union U(n-1)) end:
a:= n-> min(M(n)[]):
seq(a(n), n=1..28);

Mathematica

M[n_] := M[n] = Divisors[19^n - 1]~Complement~U[n - 1];
U[n_] := U[n] = If[n == 0, {}, M[n]~Union~U[n - 1]];
a[n_] := Min[M[n]];
Table[a[n], {n, 1, 41}] (* Jean-François Alcover, Oct 24 2022, after Alois P. Heinz *)

Crossrefs

Cf. A213224, A218339.

Sequence in context: A125723 A094543 A136511 * A108138 A119361 A133482

Adjacent sequences: A218359 A218360 A218361 * A218363 A218364 A218365

Keyword

nonn

Author

Alois P. Heinz, Oct 27 2012

Status

approved