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A218357
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Minimal order of degree-n irreducible polynomials over GF(5).
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9
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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
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OFFSET
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1,2
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COMMENTS
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a(n) < 5^n.
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LINKS
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FORMULA
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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) = {}.
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MAPLE
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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);
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MATHEMATICA
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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]];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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