

A160495


Irregular triangle of residue classes (mod pq) of primes r such that the cyclotomic polynomial Phi(pqr,x) is flat.


4



1, 14, 1, 2, 10, 11, 19, 20, 1, 7, 8, 25, 26, 32, 1, 34, 1, 2, 8, 17, 19, 20, 22, 31, 37, 38, 1, 13, 20, 22, 23, 28, 29, 31, 38, 50, 1, 2, 53, 54, 1, 2, 7, 13, 16, 23, 28, 29, 34, 41, 44, 50, 55, 56, 1, 64, 1, 7, 8, 10, 17, 19, 28, 41, 50, 52, 59, 61, 62, 68
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OFFSET

1,2


COMMENTS

A polynomial is flat if its coefficients are 1, 0, or 1. The values of pq are in sequence A046388. Each row begins with 1 and ends with pq1. For each number k in a row, the number pqk is also in the row. Row n has 2*A160496(n) terms. For the pq in sequence A160497, the row has only two terms. By Kaplan's theorems 2 and 3, only the first prime r in each residue class 1..(p1)(q1)/2 needs to be checked to determine whether the residue class produces flat cyclotomic polynomials. Is there a simplier method of finding these residue classes?


LINKS

T. D. Noe, Rows n=1..100 of triangle, flattened
Nathan Kaplan, Flat cyclotomic polynomials of order three, J. Number Theory 127 (2007), 118126.


EXAMPLE

The second row (1,2,10,11,19,20) is for pq=21. If r is a prime with r mod pq equal to one of these 6 values, then Phi(21*r,x) is flat.


CROSSREFS

Cf. A046388, A117223.
Sequence in context: A209601 A040201 A179948 * A040204 A040203 A040205
Adjacent sequences: A160492 A160493 A160494 * A160496 A160497 A160498


KEYWORD

nonn,tabf


AUTHOR

T. D. Noe, May 15 2009


STATUS

approved



