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A218361
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Minimal order of degree-n irreducible polynomials over GF(17).
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4
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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
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OFFSET
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1,2
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COMMENTS
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a(n) < 17^n.
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LINKS
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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
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FORMULA
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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).
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MAPLE
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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);
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CROSSREFS
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Cf. A213224, A218338.
Sequence in context: A307020 A071525 A157583 * A085319 A123032 A132305
Adjacent sequences: A218358 A218359 A218360 * A218362 A218363 A218364
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz, Oct 27 2012
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STATUS
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approved
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