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Search: id:A117545
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| A117545 |
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Least k such that Phi(k,n), the k-th cyclotomic polynomial evaluated at n, is prime. |
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2
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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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.
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MATHEMATICA
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Table[k=1; While[ !PrimeQ[Cyclotomic[k, n]], k++ ]; k, {n, 100}]
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CROSSREFS
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Cf. A117544 (least k such that Phi(n, k) is prime).
Sequence in context: A110269 A120964 A059674 this_sequence A047000 A139767 A057555
Adjacent sequences: A117542 A117543 A117544 this_sequence A117546 A117547 A117548
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Mar 28 2006
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