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A160338
Height (maximum absolute value of coefficients) of the n-th cyclotomic polynomial.
7
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
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
KEYWORD
nonn,nice
AUTHOR
Max Alekseyev, May 13 2009
STATUS
approved