cp's OEIS Frontend

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

%I A218356 #20 Oct 24 2022 07:44:10
%S A218356 1,4,13,5,11,7,1093,32,757,44,23,35,797161,547,143,17,1871,19,1597,25,
%T A218356 14209,67,47,224,8951,398581,109,29,59,31,683,128,299,103,71,95,
%U A218356 13097927,2851,169,352,83,43,431,115,181,188,1223,97,491,151,12853,53,107
%N A218356 Minimal order of degree-n irreducible polynomials over GF(3).
%C A218356 a(n) < 3^n.
%C A218356 For n > 2, a(n) <= A143663(n). For odd prime n, a(n) = A143663(n). - _Max Alekseyev_, Apr 30 2022
%H A218356 Max Alekseyev, <a href="/A218356/b218356.txt">Table of n, a(n) for n = 1..796</a> (first 100 terms from Alois P. Heinz)
%F A218356 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) = {}.
%F A218356 a(n) = A212906(n,1) = A213224(n,2).
%p A218356 M:= proc(n) M(n):= numtheory[divisors](3^n-1) minus U(n-1) end:
%p A218356 U:= proc(n) U(n):= `if`(n=0, {}, M(n) union U(n-1)) end:
%p A218356 a:= n-> min(M(n)[]):
%p A218356 seq(a(n), n=1..60);
%t A218356 M[n_] := M[n] = Divisors[3^n - 1]~Complement~U[n - 1];
%t A218356 U[n_] := U[n] = If[n == 0, {}, M[n]~Union~U[n - 1]];
%t A218356 a[n_] := Min[M[n]];
%t A218356 Table[a[n], {n, 1, 60}] (* _Jean-François Alcover_, Oct 24 2022, after _Alois P. Heinz_ *)
%Y A218356 Cf. A143663, A212906, A213224, A235366.
%K A218356 nonn
%O A218356 1,2
%A A218356 _Alois P. Heinz_, Oct 27 2012