cp's OEIS Frontend

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

%I A160338 #29 Nov 27 2019 12:53:24
%S A160338 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,
%T A160338 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,
%U A160338 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
%N A160338 Height (maximum absolute value of coefficients) of the n-th cyclotomic polynomial.
%C A160338 Different from A137979: first time these sequence disagree is at n=14235 with a(14235)=2 and A137979(14235)=3.
%H A160338 Max Alekseyev, <a href="/A160338/b160338.txt">Table of n, a(n) for n = 1..100000</a>
%H A160338 Alexandre Kosyak, Pieter Moree, Efthymios Sofos and Bin Zhang, <a href="https://arxiv.org/abs/1910.01039">Cyclotomic polynomials with prescribed height and prime number theory</a>, arXiv:1910.01039 [math.NT], 2019.
%H A160338 Emma Lehmer, <a href="https://doi.org/10.1090/S0002-9904-1936-06309-3">On the magnitude of the coefficients of the cyclotomic polynomial</a>, Bull. Amer. Math. Soc. 42 (1936), 389-392.
%H A160338 H. Maier, <a href="http://dx.doi.org/10.1007/978-1-4612-3464-7_22">The coefficients of cyclotomic polynomials</a>, Analytic number theory, Vol. 2 (1995), pp. 633-639, Progr. Math., 139.
%H A160338 Lola Thompson, <a href="http://arxiv.org/abs/1111.5404">Heights of divisors of x^n-1</a>, arXiv:1111.5404 [math.NT], 2011.
%H A160338 R. C. Vaughan, <a href="http://dx.doi.org/10.1307/mmj/1029001352">Bounds for the coefficients of cyclotomic polynomials</a>, Michigan Math. J. 21 (1974), 289-295 (1975).
%e A160338 a(4) = 1 because the 4th cyclotomic polynomial x^2 + 1 has height 1.
%t A160338 Table[Max@Abs@CoefficientList[Cyclotomic[n,x],x],{n,1,105}] (* from Jean-François Alcover, Apr 02 2011 *)
%o A160338 (PARI) a(n) = vecmax(abs(Vec(polcyclo(n))))
%Y A160338 Cf. A160339 (records), A160340 (indices of records), A160341.
%K A160338 nonn,nice
%O A160338 1,105
%A A160338 _Max Alekseyev_, May 13 2009