A218356 Minimal order of degree-n irreducible polynomials over GF(3).

1, 4, 13, 5, 11, 7, 1093, 32, 757, 44, 23, 35, 797161, 547, 143, 17, 1871, 19, 1597, 25, 14209, 67, 47, 224, 8951, 398581, 109, 29, 59, 31, 683, 128, 299, 103, 71, 95, 13097927, 2851, 169, 352, 83, 43, 431, 115, 181, 188, 1223, 97, 491, 151, 12853, 53, 107

Offset

1,2

Comments

a(n) < 3^n.

For n > 2, a(n) <= A143663(n). For odd prime n, a(n) = A143663(n). - Max Alekseyev, Apr 30 2022

Links

Max Alekseyev, Table of n, a(n) for n = 1..796 (first 100 terms from Alois P. Heinz)

Formula

a(n) = min(M(n)) with M(n) = {d : d|(3^n-1)} \ U(n-1) and U(n) = M(n) union U(n-1) for n>0, U(0) = {}.

a(n) = A212906(n,1) = A213224(n,2).

Maple

M:= proc(n) M(n):= numtheory[divisors](3^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..60);

Mathematica

M[n_] := M[n] = Divisors[3^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, 60}] (* Jean-François Alcover, Oct 24 2022, after Alois P. Heinz *)

Crossrefs

Cf. A143663, A212906, A213224, A235366.

Sequence in context: A170865 A320030 A191509 * A249120 A170844 A051432

Adjacent sequences: A218353 A218354 A218355 * A218357 A218358 A218359

Keyword

nonn

Author

Alois P. Heinz, Oct 27 2012

Status

approved