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

1,1

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

Mathematica

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

Crossrefs

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

Sequence in context: A059674 A367624 A342748 * A047000 A288915 A175062

Adjacent sequences: A117542 A117543 A117544 * A117546 A117547 A117548

Keyword

nonn

Author

T. D. Noe, Mar 28 2006

Status

approved