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A218361 Minimal order of degree-n irreducible polynomials over GF(17). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) < 17^n.

LINKS

Table of n, a(n) for n=1..46.

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);

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

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Last modified February 24 21:23 EST 2020. Contains 332211 sequences. (Running on oeis4.)