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

1, 3, 307, 5, 88741, 7, 25646167, 128, 19, 11, 2141993519227, 35, 212057, 22796593, 27243487, 256, 10949, 57, 229, 25, 43, 23, 47, 73, 2551, 53, 433, 5766433, 59, 31, 4093, 257, 67, 32847, 966211, 37, 149, 457, 157, 41, 83, 49, 1549, 89, 3691, 141

Offset

1,2

Comments

a(n) < 17^n.

Links

Max Alekseyev, Table of n, a(n) for n = 1..242

Eric Weisstein's World of Mathematics, Irreducible Polynomial

Eric Weisstein's World of Mathematics, Polynomial Order

Formula

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) = {}.

a(n) = A218338(n,1) = A213224(n,7).

Maple

with(numtheory):
M:= proc(n) M(n):= divisors(17^n-1) minus U(n-1) end:
U:= proc(n) U(n):= `if`(n=0, {}, M(n) union U(n-1)) end:
a:= n-> min(M(n)[]):
seq(a(n), n=1..35);

Mathematica

M[n_] := M[n] = Divisors[17^n-1] ~Complement~ U[n-1];
U[n_] := U[n] = If[n == 0, {}, M[n] ~Union~ U[n-1]];
a[n_] := a[n] = Min[M[n]];
Table[Print[n, " ", a[n]]; a[n], {n, 1, 60}] (* Jean-François Alcover, Oct 21 2022, after Maple code *)

Crossrefs

Cf. A213224, A218338.

Sequence in context: A307020 A071525 A157583 * A085319 A123032 A132305

Adjacent sequences: A218358 A218359 A218360 * A218362 A218363 A218364

Keyword

nonn

Author

Alois P. Heinz, Oct 27 2012

Status

approved