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Beatty primes from fractional powers of almost-primes (2109.00536v1)
Published 1 Sep 2021 in math.NT
Abstract: Let $\alpha>1$ be irrational and of finite type, $\beta\in\mathbb{R}$. In this paper, it is proved that for $R\geqslant13$ and any fixed $c\in(1,c_R)$, there exist infinitely many primes in the intersection of Beatty sequence $\mathcal{B}_{\alpha,\beta}$ and $\lfloor nc\rfloor$, where $c_R$ is an explicit constant depending on $R$ herein, $n$ is a natural number with at most $R$ prime factors, counted with multiplicity.