A160494 Least prime r > q such that the third-order cyclotomic polynomial Phi(pqr,x) is flat with p,q,r distinct odd primes, ordered by pq.

29, 11, 41, 71, 17, 23, 53, 23, 131, 41, 307, 509, 61, 181, 37, 191, 41, 229, 239, 89, 47, 797, 73, 571, 499, 157, 59, 643, 73, 71, 739, 373, 71, 607, 359, 419, 83, 431, 433, 89, 443, 941, 83, 1481, 109, 251, 1553, 1061, 101, 1721, 101, 401, 599, 251, 131

Offset: 1

Author

T. D. Noe, May 15 2009

Keywords

• nonn

Comments

A flat polynomial is defined to be a polynomial whose coefficients are -1, 0, or 1. Sequence A046388 gives the product pq. As proved by Kaplan, given odd primes p < q, it is always possible to find a prime r > q such that Phi(pqr,x) is flat.

Examples

			a(1)=29 because 15*29 is the least multiple of 15 that produces a flat cyclotomic polynomial.
		

Links

• Nathan Kaplan, Flat cyclotomic polynomials of order three, J. Number Theory 127 (2007), 118-126.

Crossrefs

Cf. A046388, A117223.