A117545 Least k such that Phi(k,n), the k-th cyclotomic polynomial evaluated at n, is prime.

2, 2, 1, 1, 3, 1, 5, 1, 6, 2, 9, 1, 5, 1, 3, 2, 3, 1, 19, 1, 3, 2, 5, 1, 6, 4, 3, 2, 5, 1, 7, 1, 3, 6, 21, 2, 10, 1, 6, 2, 3, 1, 5, 1, 19, 2, 10, 1, 14, 3, 6, 2, 11, 1, 6, 4, 3, 2, 3, 1, 7, 1, 5, 204, 12, 2, 6, 1, 3, 2, 3, 1, 5, 1, 3, 6, 3, 2, 5, 1, 6, 2, 5, 1, 5, 11, 7, 2, 3, 1, 6, 12, 7, 4, 7, 2, 17, 1, 3

Offset: 1

Author

T. D. Noe, Mar 28 2006

Keywords

• nonn

Comments

Note that a(n)=1 iff n-1 is prime because Phi(1,x)=x-1. For n<2048, we have the bound a(n)<251. However, a(2048) is greater than 10000. Is a(n) defined for all n? For fixed n, there are many sequences listing the k that make Phi(k,n) prime: A000043, A028491, A004061, A004062, A004063, A004023, A005808, A016054, A006032, A006033, A006034, A006035.

Links

• T. D. Noe, Table of n, a(n) for n = 1..2047

Crossrefs

Cf. A117544 (least k such that Phi(n, k) is prime).

Programs

Mathematica

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