  Consider the set $\mathcal{K}$ of integers $k$ for which there are infinitely
many primes $p$ such that $p+k$ is a power of $2$. The aim of this paper is to
show a relationship between $\mathcal{K}$ and the limits points of some set
rational numbers related to a sequence of polynomials $C_n(q)$ introduced by
Kassel and Reutenauer [KasselReutenauer].
