

A160338


Height (maximum absolute value of coefficients) of the nth cyclotomic polynomial.


6



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
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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), 389392.
H. Maier, The coefficients of cyclotomic polynomials, Analytic number theory, Vol. 2 (1995), pp. 633639, Progr. Math., 139.
Lola Thompson, Heights of divisors of x^n1, arXiv:1111.5404 [math.NT], 2011.
R. C. Vaughan, Bounds for the coefficients of cyclotomic polynomials, Michigan Math. J. 21 (1974), 289295 (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 JeanFrançois 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



