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

Author

Alois P. Heinz, Oct 27 2012

Keywords

• nonn

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)

Crossrefs

Cf. A143663, A212906, A213224, A235366.

Programs

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 *)

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).