A218364 - OEIS

%I #13 Oct 24 2022 07:44:29

%S 1,3,13,16,732541,9,49,32,14437,11,23,37,521,147,181,17,3911,19,

%T 1386659,176,637,69,131327761273,288,151,53,52813,784,59,99,36767,128,

%U 299,1973,71,304,149,16759,169,41,83,43,173,368,2613097,47,283,153,197,125,103

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

%C a(n) < 29^n.

%H Max Alekseyev, <a href="/A218364/b218364.txt">Table of n, a(n) for n = 1..222</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|(29^n-1)} \ U(n-1) and U(n) = M(n) union U(n-1) for n>0, U(0) = {}.

%F a(n) = A218341(n,1) = A213224(n,10).

%p with(numtheory):

%p M:= proc(n) M(n):= divisors(29^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..10);

%t M[n_] := M[n] = Divisors[29^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[Print[n, " ", a[n]]; a[n], {n, 1, 51}] (* _Jean-François Alcover_, Oct 24 2022, after _Alois P. Heinz_ *)

%Y Cf. A213224, A218341.

%K nonn

%O 1,2

%A _Alois P. Heinz_, Oct 27 2012