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A160493 Maximum height of the third-order cyclotomic polynomial Phi(pqr,x) with p<q<r distinct odd primes, ordered by pq. 0
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, 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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..100.

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

FORMULA

a(n) = maximum height of Phi(A046388(n)*r,x) for any prime r>q.

CROSSREFS

Cf. A046388, A117223.

Sequence in context: A085694 A258570 A257572 * A053760 A223942 A278597

Adjacent sequences:  A160490 A160491 A160492 * A160494 A160495 A160496

KEYWORD

nonn

AUTHOR

T. D. Noe, May 15 2009

STATUS

approved

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Last modified December 7 20:27 EST 2019. Contains 329849 sequences. (Running on oeis4.)