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A117544
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Least k such that Phi(n,k), the n-th cyclotomic polynomial evaluated at k, is prime.
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7
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3, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 6, 1, 4, 3, 2, 1, 2, 1, 2, 1, 4, 1, 2, 1, 1, 2, 2, 14, 3, 1, 2, 10, 2, 1, 2, 1, 25, 11, 2, 1, 5, 1, 6, 30, 11, 1, 7, 7, 2, 5, 7, 1, 3, 1, 2, 3, 1, 2, 9, 1, 85, 2, 3, 1, 3, 1, 16, 59, 7, 2, 2, 1, 2, 1, 61, 1, 7, 2, 2, 8, 5, 1, 2, 11, 4, 2, 6, 44, 4, 1, 2, 63
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OFFSET
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1,1
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COMMENTS
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Note that a(n)=1 iff n is a power of a prime.
Because every cyclotomic polynomial is irreducible, it is expected that a(n) exists for all n.
Note that if p=Phi(n,k) is prime and n>1, then p==1 (mod k). - Corrected by Robert Israel, Apr 22 2019
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LINKS
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FORMULA
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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 k fi od
end proc:
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MATHEMATICA
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Table[k=1; While[ !PrimeQ[Cyclotomic[n, k]], k++ ]; k, {n, 100}]
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PROG
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(PARI) a(n) = my(k=1); while (!isprime(polcyclo(n, k)), k++); k; \\ 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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