

A117545


Least k such that Phi(k,n), the kth 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
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OFFSET

1,1


COMMENTS

Note that a(n)=1 iff n1 is prime because Phi(1,x)=x1. 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



