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A307687
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a(n) is the first prime value of the n-th cyclotomic polynomial.
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3
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2, 2, 3, 2, 5, 3, 7, 2, 3, 11, 11, 13, 13, 43, 151, 2, 17, 46441, 19, 61681, 368089, 683, 23, 241, 5, 2731, 3, 15790321, 29, 331, 31, 2, 599479, 43691, 2984619585279628795345143571, 530713, 37, 174763, 900900900900990990990991, 61681, 41, 5419, 43, 9080418348371887359375390001
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OFFSET
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1,1
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LINKS
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FORMULA
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a(p^k) = p if p is prime.
a(n) == 1 (mod A117544(n)) for n >= 2.
a(n) = Phi(n,A117544(n)) where Phi(n,k) is the n-th cyclotomic polynomial evaluated at k.
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EXAMPLE
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a(10)=11 because the 10th cyclotomic polynomial is Phi(10,x) = x^4 - x^3 + x^2 - x + 1, and Phi(10,2)=11 is prime but Phi(10,1)=1 is not prime.
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MAPLE
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f:= proc(n) local C, x, k;
C:= unapply(numtheory:-cyclotomic(n, x), x);
for k from 1 do if isprime(C(k)) then return C(k) fi od
end proc:
map(f, [$1..100]);
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MATHEMATICA
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a[n_] := Module[{c, k}, c[x_] = Cyclotomic[n, x]; For[k = 1, True, k++, If[PrimeQ[c[k]], Return[c[k]]]]]; Array[a, 100] (* Jean-François Alcover, Apr 29 2019 *)
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PROG
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(PARI) a(n) = my(k=1, p); while (!isprime(p=polcyclo(n, k)), k++); p; \\ Michel Marcus, Apr 22 2019
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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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