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A218363
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Minimal order of degree-n irreducible polynomials over GF(23).
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4
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1, 3, 7, 5, 292561, 9, 29, 64, 19, 31, 121, 35, 47691619, 71, 2047927, 17, 103, 27, 2129, 25, 43, 363, 461, 448, 6551, 143074857, 4591, 145, 233, 151, 40888990028603, 193, 67, 239, 8484269, 73, 1925658337781, 6387, 333841333, 1600, 83, 129, 173, 605, 5558659
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OFFSET
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1,2
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COMMENTS
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a(n) < 23^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|(23^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(23^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..30);
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MATHEMATICA
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M[n_] := M[n] = Divisors[23^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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