A307687 a(n) is the first prime value of the n-th cyclotomic polynomial.

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

Offset: 1

Author

Robert Israel, Apr 22 2019

Keywords

• nonn

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..426

Crossrefs

Cf. A117544.

Programs

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 C(k) fi od
end proc:
map(f, [$1..100]);

Mathematica

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 *)

PARI

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

Formula

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.