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A218358 Minimal order of degree-n irreducible polynomials over GF(7).

%I A218358 #17 Feb 16 2025 08:33:18
%S A218358 1,4,9,5,2801,36,29,64,27,11,1123,13,16148168401,113,31,17,14009,108,
%T A218358 419,55,261,23,47,73,2551,53,81,145,59,99,311,256,3631,56036,81229,
%U A218358 135,223,1676,486643,41,83,1017,166003607842448777,115,837,188,13722816749522711
%N A218358 Minimal order of degree-n irreducible polynomials over GF(7).
%C A218358 a(n) < 7^n.
%H A218358 Max Alekseyev, <a href="/A218358/b218358.txt">Table of n, a(n) for n = 1..430</a>
%H A218358 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IrreduciblePolynomial.html">Irreducible Polynomial</a>
%H A218358 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PolynomialOrder.html">Polynomial Order</a>
%F A218358 a(n) = min(M(n)) with M(n) = {d : d|(7^n-1)} \ U(n-1) and U(n) = M(n) union U(n-1) for n>0, U(0) = {}.
%F A218358 a(n) = A212486(n,1) = A213224(n,4).
%p A218358 with(numtheory):
%p A218358 M:= proc(n) M(n):= divisors(7^n-1) minus U(n-1) end:
%p A218358 U:= proc(n) U(n):= `if`(n=0, {}, M(n) union U(n-1)) end:
%p A218358 a:= n-> min(M(n)[]):
%p A218358 seq(a(n), n=1..42);
%t A218358 M[n_] := M[n] = Divisors[7^n - 1]~Complement~U[n - 1];
%t A218358 U[n_] := U[n] = If[n == 0, {}, M[n]~Union~U[n - 1]];
%t A218358 a[n_] := Min[M[n]];
%t A218358 Table[a[n], {n, 1, 47}] (* _Jean-François Alcover_, Oct 24 2022, after _Alois P. Heinz_ *)
%Y A218358 Cf. A057954, A074249, A212486, A213224.
%K A218358 nonn
%O A218358 1,2
%A A218358 _Alois P. Heinz_, Oct 27 2012