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A117544
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Least k such that Phi(n,k), the n-th cyclotomic polynomial evaluated at k, is prime.
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2
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3, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 6, 1, 4, 3, 2, 1, 2, 1, 2, 1, 4, 1, 2, 1, 1, 2, 2, 14, 3, 1, 2, 10, 2, 1, 2, 1, 25, 11, 2, 1, 5, 1, 6, 30, 11, 1, 7, 7, 2, 5, 7, 1, 3, 1, 2, 3, 1, 2, 9, 1, 85, 2, 3, 1, 3, 1, 16, 59, 7, 2, 2, 1, 2, 1, 61, 1, 7, 2, 2, 8, 5, 1, 2, 11, 4, 2, 6, 44, 4, 1, 2, 63
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Note that a(n)=1 iff n is a power of a prime. Because every cyclotomic polynomial is irreducible, it is expected that a(n) exists for all n. Note that if p=Phi(n,k) is prime, then p=1 (mod n).
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
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MATHEMATICA
| Table[k=1; While[ !PrimeQ[Cyclotomic[n, k]], k++ ]; k, {n, 100}]
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CROSSREFS
| Cf. A117545 (least k such that Phi(k, n) is prime).
Sequence in context: A016565 A051714 A023593 * A030393 A109393 A030348
Adjacent sequences: A117541 A117542 A117543 * A117545 A117546 A117547
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KEYWORD
| nonn
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Mar 28 2006
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