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

1,1

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.

Links

Table of n, a(n) for n=1..55.

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

Example

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

Crossrefs

Cf. A046388, A117223.

Sequence in context: A070714 A040816 A336061 * A332940 A165769 A040815

Adjacent sequences: A160491 A160492 A160493 * A160495 A160496 A160497

Keyword

nonn

Author

T. D. Noe, May 15 2009

Status

approved