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A218358
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Minimal order of degree-n irreducible polynomials over GF(7).
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8
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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
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OFFSET
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1,2
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COMMENTS
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a(n) < 7^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|(7^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(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);
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MATHEMATICA
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M[n_] := M[n] = Divisors[7^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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