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

%I A218364 #14 Feb 16 2025 08:33:18
%S A218364 1,3,13,16,732541,9,49,32,14437,11,23,37,521,147,181,17,3911,19,
%T A218364 1386659,176,637,69,131327761273,288,151,53,52813,784,59,99,36767,128,
%U A218364 299,1973,71,304,149,16759,169,41,83,43,173,368,2613097,47,283,153,197,125,103
%N A218364 Minimal order of degree-n irreducible polynomials over GF(29).
%C A218364 a(n) < 29^n.
%H A218364 Max Alekseyev, <a href="/A218364/b218364.txt">Table of n, a(n) for n = 1..222</a>
%H A218364 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IrreduciblePolynomial.html">Irreducible Polynomial</a>
%H A218364 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PolynomialOrder.html">Polynomial Order</a>
%F A218364 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) = {}.
%F A218364 a(n) = A218341(n,1) = A213224(n,10).
%p A218364 with(numtheory):
%p A218364 M:= proc(n) M(n):= divisors(29^n-1) minus U(n-1) end:
%p A218364 U:= proc(n) U(n):= `if`(n=0, {}, M(n) union U(n-1)) end:
%p A218364 a:= n-> min(M(n)[]):
%p A218364 seq(a(n), n=1..10);
%t A218364 M[n_] := M[n] = Divisors[29^n - 1]~Complement~U[n - 1];
%t A218364 U[n_] := U[n] = If[n == 0, {}, M[n]~Union~U[n - 1]];
%t A218364 a[n_] := Min[M[n]];
%t A218364 Table[Print[n, " ", a[n]]; a[n], {n, 1, 51}] (* _Jean-François Alcover_, Oct 24 2022, after _Alois P. Heinz_ *)
%Y A218364 Cf. A213224, A218341.
%K A218364 nonn
%O A218364 1,2
%A A218364 _Alois P. Heinz_, Oct 27 2012