id:A117544 - OEIS Search Results

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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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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; listen)

	OFFSET	`1,1`
	COMMENT	`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).`
	LINKS	`T. D. Noe, Table of n, a(n) for n=1..1000`
	MATHEMATICA	`Table[k=1; While[ !PrimeQ[Cyclotomic[n, k]], k++ ]; k, {n, 100}]`
	CROSSREFS	`Cf. A117545 (least k such that Phi(k, n) is prime).` `Sequence in context: A016565 A051714 A023593 this_sequence A030393 A109393 A030348` `Adjacent sequences: A117541 A117542 A117543 this_sequence A117545 A117546 A117547`
	KEYWORD	`nonn`
	AUTHOR	`T. D. Noe (noe(AT)sspectra.com), Mar 28 2006`

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Last modified November 18 20:14 EST 2008. Contains 147244 sequences.

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