A160338 Height (maximum absolute value of coefficients) of the n-th cyclotomic polynomial.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2

Offset

1,105

Comments

Different from A137979: first time these sequence disagree is at n=14235 with a(14235)=2 and A137979(14235)=3.

Links

Max Alekseyev, Table of n, a(n) for n = 1..100000

Alexandre Kosyak, Pieter Moree, Efthymios Sofos and Bin Zhang, Cyclotomic polynomials with prescribed height and prime number theory, arXiv:1910.01039 [math.NT], 2019.

Emma Lehmer, On the magnitude of the coefficients of the cyclotomic polynomial, Bull. Amer. Math. Soc. 42 (1936), 389-392.

H. Maier, The coefficients of cyclotomic polynomials, Analytic number theory, Vol. 2 (1995), pp. 633-639, Progr. Math., 139.

Lola Thompson, Heights of divisors of x^n-1, arXiv:1111.5404 [math.NT], 2011.

R. C. Vaughan, Bounds for the coefficients of cyclotomic polynomials, Michigan Math. J. 21 (1974), 289-295 (1975).

Example

a(4) = 1 because the 4th cyclotomic polynomial x^2 + 1 has height 1.

Mathematica

Table[Max@Abs@CoefficientList[Cyclotomic[n, x], x], {n, 1, 105}] (* from Jean-François Alcover, Apr 02 2011 *)

Prog

(PARI) a(n) = vecmax(abs(Vec(polcyclo(n))))

Crossrefs

Cf. A160339 (records), A160340 (indices of records), A160341.

Sequence in context: A112316 A112802 A137979 * A216579 A229878 A235145

Adjacent sequences: A160335 A160336 A160337 * A160339 A160340 A160341

Keyword

nonn,nice

Author

Max Alekseyev, May 13 2009

Status

approved