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 15307638.
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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 socalled 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:  Faculties > Sciences > School of Mathematics Statistics and Actuarial Science 
Depositing User:  Andrew N W Hone 
Date Deposited:  10 Oct 2018 14:15 UTC 
Last Modified:  29 May 2019 21:16 UTC 
Resource URI:  https://kar.kent.ac.uk/id/eprint/69496 (The current URI for this page, for reference purposes) 
Hone, Andrew N.W.:  https://orcid.org/0000000197807369 
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