A189408 Least k where Phi(k) has height greater than k^n, where Phi(k) is the k-th cyclotomic polynomial and the height is the largest absolute value of the coefficients.

1181895, 43730115, 416690995, 1880394945

Offset

1,1

Comments

Arnold & Monagan compute this sequence to demonstrate their fast algorithm for computing cyclotomic polynomials.

This sequence is infinite because (the supremum of) A160338 grows exponentially.

Links

Table of n, a(n) for n=1..4.

Andrew Arnold and Michael Monagan, A high-performance algorithm for calculating cyclotomic polynomials, PASCO 2010. doi:10.1145/1837210.1837228

Andrew Arnold and Michael Monagan, A fast recursive algorithm for computing cyclotomic polynomials, ACM Commun. Comput. Algebra 44:3/4 (2010), pp. 89-90. doi:10.1145/1940475.1940479

Andrew Arnold, Michael Monagan, Calculating cyclotomic polynomials, Mathematics of Computation 80 (276) (2011) 2359-2379 preprint.

Andrew Arnold and Michael Monagan, Cyclotomic Polynomials

Crossrefs

Subsequence of A160340. Cf. A160338, A108975.

Sequence in context: A210411 A204777 A236718 * A251988 A233469 A237849

Adjacent sequences: A189405 A189406 A189407 * A189409 A189410 A189411

Keyword

nonn,hard,more

Author

Charles R Greathouse IV, Apr 21 2011

Status

approved