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A117545 Least k such that Phi(k,n), the k-th cyclotomic polynomial evaluated at n, is prime. 5
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 (list; graph; refs; listen; history; text; internal format)
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: A157522 A059674 A342748 * A047000 A288915 A175062

Adjacent sequences:  A117542 A117543 A117544 * A117546 A117547 A117548

KEYWORD

nonn

AUTHOR

T. D. Noe, Mar 28 2006

STATUS

approved

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Last modified October 16 03:52 EDT 2021. Contains 348035 sequences. (Running on oeis4.)