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A218361 Minimal order of degree-n irreducible polynomials over GF(17).

%I A218361 #18 Feb 26 2025 09:02:44
%S A218361 1,3,307,5,88741,7,25646167,128,19,11,2141993519227,35,212057,
%T A218361 22796593,27243487,256,10949,57,229,25,43,23,47,73,2551,53,433,
%U A218361 5766433,59,31,4093,257,67,32847,966211,37,149,457,157,41,83,49,1549,89,3691,141
%N A218361 Minimal order of degree-n irreducible polynomials over GF(17).
%C A218361 a(n) < 17^n.
%H A218361 Max Alekseyev, <a href="/A218361/b218361.txt">Table of n, a(n) for n = 1..372</a>
%H A218361 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IrreduciblePolynomial.html">Irreducible Polynomial</a>
%H A218361 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PolynomialOrder.html">Polynomial Order</a>
%F A218361 a(n) = min(M(n)) with M(n) = {d : d|(17^n-1)} \ U(n-1) and U(n) = M(n) union U(n-1) for n>0, U(0) = {}.
%F A218361 a(n) = A218338(n,1) = A213224(n,7).
%p A218361 with(numtheory):
%p A218361 M:= proc(n) M(n):= divisors(17^n-1) minus U(n-1) end:
%p A218361 U:= proc(n) U(n):= `if`(n=0, {}, M(n) union U(n-1)) end:
%p A218361 a:= n-> min(M(n)[]):
%p A218361 seq(a(n), n=1..35);
%t A218361 M[n_] := M[n] = Divisors[17^n-1] ~Complement~ U[n-1];
%t A218361 U[n_] := U[n] = If[n == 0, {}, M[n] ~Union~ U[n-1]];
%t A218361 a[n_] := a[n] = Min[M[n]];
%t A218361 Table[Print[n, " ", a[n]]; a[n], {n, 1, 60}] (* _Jean-François Alcover_, Oct 21 2022, after Maple code *)
%Y A218361 Cf. A213224, A218338.
%K A218361 nonn
%O A218361 1,2
%A A218361 _Alois P. Heinz_, Oct 27 2012