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A218357 Minimal order of degree-n irreducible polynomials over GF(5). 2
1, 3, 31, 13, 11, 7, 19531, 32, 19, 33, 12207031, 91, 305175781, 29, 181, 17, 409, 27, 191, 41, 379, 23, 8971, 224, 101, 5227, 109, 377, 59, 61, 1861, 128, 199, 1227, 211, 37, 149, 573, 79, 241, 2238236249, 43, 1644512641, 89, 209, 47, 177635683940025046467781066894531 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) < 5^n.

LINKS

Table of n, a(n) for n=1..47.

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|(5^n-1)} \ U(n-1) and U(n) = M(n) union U(n-1) for n>0, U(0) = {}.

a(n) = A212485(n,1) = A213224(n,3).

MAPLE

with(numtheory):

M:= proc(n) M(n):= divisors(5^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..47);

MATHEMATICA

M[n_] := M[n] = Divisors[5^n - 1] ~Complement~ U[n-1];

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

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

Table[a[n], {n, 1, 47}] (* Jean-Fran├žois Alcover, Mar 24 2017, translated from Maple *)

CROSSREFS

Cf. A212485, A213224.

Sequence in context: A322777 A089281 A212729 * A090543 A215946 A139090

Adjacent sequences:  A218354 A218355 A218356 * A218358 A218359 A218360

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 27 2012

STATUS

approved

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Last modified January 28 03:34 EST 2020. Contains 331315 sequences. (Running on oeis4.)