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 pq-1. For each number k in a row, the number pq-k 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..(p-1)(q-1)/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), 118-126.
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
KEYWORD
nonn,tabf
AUTHOR
T. D. Noe, May 15 2009
STATUS
approved