A218364 Minimal order of degree-n irreducible polynomials over GF(29).

1, 3, 13, 16, 732541, 9, 49, 32, 14437, 11, 23, 37, 521, 147, 181, 17, 3911, 19, 1386659, 176, 637, 69, 131327761273, 288, 151, 53, 52813, 784, 59, 99, 36767, 128, 299, 1973, 71, 304, 149, 16759, 169, 41, 83, 43, 173, 368, 2613097, 47, 283, 153, 197, 125, 103

Offset

1,2

Comments

a(n) < 29^n.

Links

Max Alekseyev, Table of n, a(n) for n = 1..222

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|(29^n-1)} \ U(n-1) and U(n) = M(n) union U(n-1) for n>0, U(0) = {}.

a(n) = A218341(n,1) = A213224(n,10).

Maple

with(numtheory):
M:= proc(n) M(n):= divisors(29^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..10);

Mathematica

M[n_] := M[n] = Divisors[29^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[Print[n, " ", a[n]]; a[n], {n, 1, 51}] (* Jean-François Alcover, Oct 24 2022, after Alois P. Heinz *)

Crossrefs

Cf. A213224, A218341.

Sequence in context: A041297 A041815 A042589 * A107922 A119889 A038956

Adjacent sequences: A218361 A218362 A218363 * A218365 A218366 A218367

Keyword

nonn

Author

Alois P. Heinz, Oct 27 2012

Status

approved