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A072883
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Least k >= 1 such that k^n + n is prime, or 0 if no such k exists.
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8
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1, 1, 2, 1, 2, 1, 16, 3, 2, 1, 32, 1, 118, 417, 2, 1, 14, 1, 22, 81, 76, 1, 12, 55, 28, 15, 0, 1, 110, 1, 232, 117, 230, 3, 12, 1, 4, 375, 2, 1, 48, 1, 46, 15, 218, 1, 78, 7, 100, 993, 28, 1, 624, 13, 252, 183, 226, 1, 104, 1, 1348, 777, 1294, 0, 1806, 1, 306, 1815, 10, 1, 30, 1
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OFFSET
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1,3
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COMMENTS
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Because the polynomial x^n + n is reducible for n in A097792, a(27) and a(64) are 0. Although x^4 + 4 is reducible, the factor x^2 - 2x + 2 is 1 for x=1. - T. D. Noe, Aug 24 2004
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LINKS
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MATHEMATICA
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Table[If[MemberQ[{27, 64}, n], 0, k=1; While[ !PrimeQ[k^n+n], k++ ]; k], {n, 100}]
(* Second program: *)
okQ[n_] := n == 4 || IrreduciblePolynomialQ[x^n + n];
a[n_] := If[!okQ[n], 0, s = 1; While[!PrimeQ[s^n + n], s++]; s];
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PROG
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(PARI) isok(n) = (n==4) || polisirreducible(x^n+n);
a(n) = if (!isok(n), 0, my(s=1); while(!isprime(s^n+n), s++); s); \\ adapted by Michel Marcus, Jan 15 2019
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CROSSREFS
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Cf. A097792 (n such that x^n + n is reducible).
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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