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A160338 Height (maximum absolute value of coefficients) of the n-th cyclotomic polynomial. 6


%S 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,

%T 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,

%U 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2

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

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

%H Max Alekseyev, <a href="/A160338/b160338.txt">Table of n, a(n) for n = 1..100000</a>

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

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

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

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

%K nonn,nice

%O 1,105

%A _Max Alekseyev_, May 13 2009

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Last modified April 22 14:23 EDT 2019. Contains 322349 sequences. (Running on oeis4.)