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A218359 Minimal order of degree-n irreducible polynomials over GF(11). 2
1, 3, 7, 16, 25, 9, 43, 32, 1772893, 75, 15797, 13, 1093, 129, 175, 17, 50544702849929377, 27, 6115909044841454629, 400, 49, 23, 829, 224, 125, 53, 5559917315850179173, 29, 523, 31, 50159, 128, 661, 71707, 211, 351, 2591, 191, 79, 41, 83, 147, 1416258521793067 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) < 11^n.

LINKS

Table of n, a(n) for n=1..43.

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|(11^n-1)} \ U(n-1) and U(n) = M(n) union U(n-1) for n>0, U(0) = {}.

a(n) = A218336(n,1) = A213224(n,5).

MAPLE

with(numtheory):

M:= proc(n) M(n):= divisors(11^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. A213224, A218336.

Sequence in context: A218276 A221025 A036666 * A117491 A211379 A213180

Adjacent sequences:  A218356 A218357 A218358 * A218360 A218361 A218362

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 27 2012

STATUS

approved

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Last modified January 24 16:47 EST 2020. Contains 331209 sequences. (Running on oeis4.)