Hone, Andrew N.W., Jeffery, L. Edson, Selcoe, Robert G. (2018) On a Family of Sequences Related to Chebyshev Polynomials. Journal of Integer Sequences, 21 . 18.7.2. ISSN 1530-7638. (KAR id:69496)
PDF
Publisher pdf
Language: English |
|
Download this file (PDF/439kB) |
![]() |
Request a format suitable for use with assistive technology e.g. a screenreader | |
Official URL: https://cs.uwaterloo.ca/journals/JIS/VOL21/Hone/ho... |
Abstract
We consider the appearance of primes in a family of linear recurrence sequences
labelled by a positive integer n. The terms of each sequence correspond to a particular
class of Lehmer numbers, or (viewing them as polynomials in n) dilated versions of the
so-called Chebyshev polynomials of the fourth kind, also known as airfoil polynomials.
We prove that when the value of n is given by a dilated Chebyshev polynomial of the
first kind evaluated at a suitable integer, either the sequence contains a single prime, or no term is prime. For all other values of n, we conjecture that the sequence contains
infinitely many primes, whose distribution has analogous properties to the distribution
of Mersenne primes among the Mersenne numbers. Similar results are obtained for
the sequences associated with negative integers n, which correspond to Chebyshev
polynomials of the third kind, and to another family of Lehmer numbers.
Item Type: | Article |
---|---|
Subjects: | Q Science > QA Mathematics (inc Computing science) |
Divisions: | Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science |
Depositing User: | Andrew Hone |
Date Deposited: | 10 Oct 2018 14:15 UTC |
Last Modified: | 09 Dec 2022 06:58 UTC |
Resource URI: | https://kar.kent.ac.uk/id/eprint/69496 (The current URI for this page, for reference purposes) |
- Link to SensusAccess
- Export to:
- RefWorks
- EPrints3 XML
- BibTeX
- CSV
- Depositors only (login required):