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

1,1

Links

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

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.

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A117544.

Sequence in context: A280990 A327667 A256267 * A281121 A220949 A029656

Adjacent sequences: A307684 A307685 A307686 * A307688 A307689 A307690

Keyword

nonn

Author

Robert Israel, Apr 22 2019

Status

approved