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A218359 Minimal order of degree-n irreducible polynomials over GF(11).

%I A218359 #20 Feb 16 2025 08:33:18
%S A218359 1,3,7,16,25,9,43,32,1772893,75,15797,13,1093,129,175,17,
%T A218359 50544702849929377,27,6115909044841454629,400,49,23,829,224,125,53,
%U A218359 5559917315850179173,29,523,31,50159,128,661,71707,211,351,2591,191,79,41,83,147,1416258521793067
%N A218359 Minimal order of degree-n irreducible polynomials over GF(11).
%C A218359 a(n) < 11^n.
%H A218359 Max Alekseyev, <a href="/A218359/b218359.txt">Table of n, a(n) for n = 1..330</a>
%H A218359 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IrreduciblePolynomial.html">Irreducible Polynomial</a>
%H A218359 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PolynomialOrder.html">Polynomial Order</a>
%F A218359 a(n) = min(M(n)) with M(n) = {d : d|(11^n-1)} \ U(n-1) and U(n) = M(n) union U(n-1) for n>0, U(0) = {}.
%F A218359 a(n) = A218336(n,1) = A213224(n,5).
%p A218359 with(numtheory):
%p A218359 M:= proc(n) M(n):= divisors(11^n-1) minus U(n-1) end:
%p A218359 U:= proc(n) U(n):= `if`(n=0, {}, M(n) union U(n-1)) end:
%p A218359 a:= n-> min(M(n)[]):
%p A218359 seq(a(n), n=1..42);
%t A218359 M[n_] := M[n] = Divisors[11^n - 1]~Complement~U[n - 1];
%t A218359 U[n_] := U[n] = If[n == 0, {}, M[n]~Union~U[n - 1]];
%t A218359 a[n_] := Min[M[n]];
%t A218359 Table[a[n], {n, 1, 43}] (* _Jean-François Alcover_, Oct 24 2022, after _Alois P. Heinz_ *)
%Y A218359 Cf. A213224, A218336, A274910.
%K A218359 nonn
%O A218359 1,2
%A A218359 _Alois P. Heinz_, Oct 27 2012