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A218358 Minimal order of degree-n irreducible polynomials over GF(7). 2
1, 4, 9, 5, 2801, 36, 29, 64, 27, 11, 1123, 13, 16148168401, 113, 31, 17, 14009, 108, 419, 55, 261, 23, 47, 73, 2551, 53, 81, 145, 59, 99, 311, 256, 3631, 56036, 81229, 135, 223, 1676, 486643, 41, 83, 1017, 166003607842448777, 115, 837, 188, 13722816749522711 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) < 7^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|(7^n-1)} \ U(n-1) and U(n) = M(n) union U(n-1) for n>0, U(0) = {}.

a(n) = A212486(n,1) = A213224(n,4).

MAPLE

with (numtheory):

M:= proc(n) M(n):= divisors(7^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..42);

CROSSREFS

Cf. A212486, A213224.

Sequence in context: A137807 A163103 A019688 * A196403 A238557 A271181

Adjacent sequences:  A218355 A218356 A218357 * A218359 A218360 A218361

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 27 2012

STATUS

approved

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Last modified January 23 22:36 EST 2020. Contains 331177 sequences. (Running on oeis4.)