A218359 Minimal order of degree-n irreducible polynomials over GF(11).

1, 3, 7, 16, 25, 9, 43, 32, 1772893, 75, 15797, 13, 1093, 129, 175, 17, 50544702849929377, 27, 6115909044841454629, 400, 49, 23, 829, 224, 125, 53, 5559917315850179173, 29, 523, 31, 50159, 128, 661, 71707, 211, 351, 2591, 191, 79, 41, 83, 147, 1416258521793067

Offset

1,2

Comments

a(n) < 11^n.

Links

Max Alekseyev, Table of n, a(n) for n = 1..330

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|(11^n-1)} \ U(n-1) and U(n) = M(n) union U(n-1) for n>0, U(0) = {}.

a(n) = A218336(n,1) = A213224(n,5).

Maple

with(numtheory):
M:= proc(n) M(n):= divisors(11^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[11^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, 43}] (* Jean-François Alcover, Oct 24 2022, after Alois P. Heinz *)

Crossrefs

Cf. A213224, A218336, A274910.

Sequence in context: A218276 A221025 A036666 * A117491 A211379 A213180

Adjacent sequences: A218356 A218357 A218358 * A218360 A218361 A218362

Keyword

nonn

Author

Alois P. Heinz, Oct 27 2012

Status

approved