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A125973
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Smallest k such that k^n + k^(n-1) - 1 is prime.
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11
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2, 2, 2, 2, 2, 3, 2, 2, 14, 4, 7, 2, 38, 6, 7, 3, 4, 10, 2, 9, 74, 6, 10, 7, 4, 61, 20, 4, 5, 9, 6, 16, 6, 8, 2, 9, 4, 10, 2, 48, 44, 163, 9, 2, 95, 3, 27, 70, 6, 26, 57, 9, 6, 8, 207, 2, 27, 15, 45, 7, 69, 199, 55, 16, 2, 5, 12, 43, 137, 39, 9, 57, 5, 20, 4, 115, 2, 103, 45, 15, 20, 109
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OFFSET
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1,1
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COMMENTS
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The polynomial x^n + x^(n-1) - 1 is irreducible over the rationals (see Ljunggren link), so the Bunyakovsky conjecture implies that a(n) always exists. - Robert Israel, Nov 16 2016
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LINKS
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EXAMPLE
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Consider n = 6. k^6 + k^5 - 1 evaluates to 1, 95, 971 for k = 1, 2, 3. Only the last of these numbers is prime, hence a(6) = 3.
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MAPLE
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f:= proc(n) local k;
for k from 2 do if isprime(k^n+k^(n-1)-1) then return k fi od
end proc:
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MATHEMATICA
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a[n_] := For[k = 2, True, k++, If[PrimeQ[k^n + k^(n-1) - 1], Return[k]]];
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PROG
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(PARI) {m=82; for(n=1, m, k=1; while(!isprime(k^n+k^(n-1)-1), k++); print1(k, ", "))} \\ Klaus Brockhaus, Dec 17 2006
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CROSSREFS
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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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