cp's OEIS Frontend

A160493 Maximum height of the third-order cyclotomic polynomial Phi(pqr,x) with p distinct odd primes, ordered by pq.

%I A160493 #9 Apr 14 2017 03:00:07
%S A160493 2,2,2,3,2,2,3,2,3,2,4,3,2,3,2,3,2,3,4,2,2,4,2,6,3,3,2,4,2,2,3,5,2,4,
%T A160493 3,7,2,3,4,2,7,3,2,5,2,3,4,3,2,4,2,3,7,4,2,3,2,7,2,9,2,4,3,2,6,3,3,4,
%U A160493 7,2,7,2,3,8,6,2,4,3,2,4,11,3,2,7,2,4,2,5,7,3,2,10,4,2,3,4,3,6,2,9
%N A160493 Maximum height of the third-order cyclotomic polynomial Phi(pqr,x) with p<q<r distinct odd primes, ordered by pq.
%C A160493 The height of a polynomial is the maximum of the absolute value of its coefficients. Sequence A046388 gives increasing values of pq. As proved by Kaplan, to compute the maximum height of Phi(pqr,x) for any prime r, there are only (p-1)(q-1)/2 values of r to consider. The set s of values of r can be taken to be primes greater than q such that the union of s and -s (mod pq) contains every number less than and coprime to pq. It appears that when p=3, the maximum height is 2; when p=5, the maximum is 3; when p=7, the maximum is 3 or 4; and when p=11, the maximum is no greater than 7.
%H A160493 Nathan Kaplan, <a href="https://doi.org/10.1016/j.jnt.2007.01.008">Flat cyclotomic polynomials of order three</a>, J. Number Theory 127 (2007), 118-126.
%F A160493 a(n) = maximum height of Phi(A046388(n)*r,x) for any prime r>q.
%Y A160493 Cf. A046388, A117223.
%K A160493 nonn
%O A160493 1,1
%A A160493 _T. D. Noe_, May 15 2009