On sums of primes from Beatty sequences

Abstract

Let $k\ge 2$ and ${\alpha }_1,{\beta }_1,...,{\alpha }_k,{\beta }_k$ be reals such that the ${\alpha }_i$'s are irrational and greater than 1. Suppose further that some ratio ${\alpha }_i/{\alpha }_j$ is irrational. We study the representations of an integer $n$ in the form $$p_1+p_2+...+p_k=n,$$ where $p_i$ is a prime from the Beatty sequence $${\mathcal{B}}_i=\left\{n\in \mathbb{N}:n=[{\alpha }_{i}m+{\beta }_i]\text{for some}m\in \mathbb{Z}\right\}.$$

References in corpus (1)

• Representations of integers as sums of primes from a Beatty sequence

Cited by in corpus (1)

• Representations of integers as sums of primes from a Beatty sequence