On a Family of Sequences Related to Chebyshev Polynomials

We consider the appearance of primes in a family of linear recurrence sequences

class of Lehmer numbers, or (viewing them as polynomials in n) dilated versions of the

We prove that when the value of n is given by a dilated Chebyshev polynomial of the

infinitely many primes, whose distribution has analogous properties to the distribution

the sequences associated with negative integers n, which correspond to Chebyshev

polynomials of the third kind, and to another family of Lehmer numbers.