%I #16 Jan 03 2024 23:56:54

%S 1,4,9,5,2801,36,29,64,27,11,1123,13,16148168401,113,31,17,14009,108,

%T 419,55,261,23,47,73,2551,53,81,145,59,99,311,256,3631,56036,81229,

%U 135,223,1676,486643,41,83,1017,166003607842448777,115,837,188,13722816749522711

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

%C a(n) < 7^n.

%H Max Alekseyev, <a href="/A218358/b218358.txt">Table of n, a(n) for n = 1..430</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/IrreduciblePolynomial.html">Irreducible Polynomial</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PolynomialOrder.html">Polynomial Order</a>

%F 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 a(n) = A212486(n,1) = A213224(n,4).

%p with(numtheory):

%p M:= proc(n) M(n):= divisors(7^n-1) minus U(n-1) end:

%p U:= proc(n) U(n):= `if`(n=0, {}, M(n) union U(n-1)) end:

%p a:= n-> min(M(n)[]):

%p seq(a(n), n=1..42);

%t M[n_] := M[n] = Divisors[7^n - 1]~Complement~U[n - 1];

%t U[n_] := U[n] = If[n == 0, {}, M[n]~Union~U[n - 1]];

%t a[n_] := Min[M[n]];

%t Table[a[n], {n, 1, 47}] (* _Jean-François Alcover_, Oct 24 2022, after _Alois P. Heinz_ *)

%Y Cf. A057954, A074249, A212486, A213224.

%K nonn

%O 1,2

%A _Alois P. Heinz_, Oct 27 2012