A218358 Minimal order of degree-n irreducible polynomials over GF(7).

1, 4, 9, 5, 2801, 36, 29, 64, 27, 11, 1123, 13, 16148168401, 113, 31, 17, 14009, 108, 419, 55, 261, 23, 47, 73, 2551, 53, 81, 145, 59, 99, 311, 256, 3631, 56036, 81229, 135, 223, 1676, 486643, 41, 83, 1017, 166003607842448777, 115, 837, 188, 13722816749522711

Offset

1,2

Comments

a(n) < 7^n.

Links

Max Alekseyev, Table of n, a(n) for n = 1..430

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|(7^n-1)} \ U(n-1) and U(n) = M(n) union U(n-1) for n>0, U(0) = {}.

a(n) = A212486(n,1) = A213224(n,4).

Maple

with(numtheory):
M:= proc(n) M(n):= divisors(7^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..42);

Mathematica

M[n_] := M[n] = Divisors[7^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, 47}] (* Jean-François Alcover, Oct 24 2022, after Alois P. Heinz *)

Crossrefs

Cf. A057954, A074249, A212486, A213224.

Sequence in context: A163103 A019688 A365725 * A340127 A196403 A238557

Adjacent sequences: A218355 A218356 A218357 * A218359 A218360 A218361

Keyword

nonn

Author

Alois P. Heinz, Oct 27 2012

Status

approved