A117544 Least k such that Phi(n,k), the n-th cyclotomic polynomial evaluated at k, is prime.

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

Offset

1,1

Comments

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

Links

Jinyuan Wang, Table of n, a(n) for n = 1..5000 (terms 1..1000 from T. D. Noe)

Formula

Phi(n, a(n)) = A307687(n). - Robert Israel, Apr 22 2019

Maple

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:
map(f, [$1..200]); # Robert Israel, Apr 22 2019

Mathematica

Table[k=1; While[ !PrimeQ[Cyclotomic[n, k]], k++ ]; k, {n, 100}]

Prog

(PARI) a(n) = my(k=1); while (!isprime(polcyclo(n, k)), k++); k; \\ Michel Marcus, Apr 22 2019

Crossrefs

Cf. A085398, A117545 (least k such that Phi(k, n) is prime), A307687.

Sequence in context: A023593 A353755 A353784 * A030393 A328391 A109393

Adjacent sequences: A117541 A117542 A117543 * A117545 A117546 A117547

Keyword

nonn

Author

T. D. Noe, Mar 28 2006

Status

approved