%I #24 Dec 17 2022 07:18:08
%S 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,
%T 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,
%U 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
%N Least k such that Phi(n,k), the n-th cyclotomic polynomial evaluated at k, is prime.
%C Note that a(n)=1 iff n is a power of a prime.
%C Because every cyclotomic polynomial is irreducible, it is expected that a(n) exists for all n.
%C Note that if p=Phi(n,k) is prime and n>1, then p==1 (mod k). - Corrected by _Robert Israel_, Apr 22 2019
%H Jinyuan Wang, <a href="/A117544/b117544.txt">Table of n, a(n) for n = 1..5000</a> (terms 1..1000 from T. D. Noe)
%F Phi(n, a(n)) = A307687(n). - _Robert Israel_, Apr 22 2019
%p f:= proc(n) local C, x, k;
%p C:= unapply(numtheory:-cyclotomic(n, x), x);
%p for k from 1 do if isprime(C(k)) then return k fi od
%p end proc:
%p map(f, [$1..200]); # _Robert Israel_, Apr 22 2019
%t Table[k=1; While[ !PrimeQ[Cyclotomic[n,k]], k++ ]; k, {n,100}]
%o (PARI) a(n) = my(k=1); while (!isprime(polcyclo(n, k)), k++); k; \\ _Michel Marcus_, Apr 22 2019
%Y Cf. A085398, A117545 (least k such that Phi(k, n) is prime), A307687.
%K nonn
%O 1,1
%A _T. D. Noe_, Mar 28 2006