Beatty primes from fractional powers of almost-primes

Abstract

Let α>1 be irrational and of finite type, β∈R. In this paper, it is proved that for R⩾13 and any fixed c∈(1,cR), there exist infinitely many primes in the intersection of Beatty sequence Bα,β and ⌊nc⌋, where cR is an explicit constant depending on R herein, n is a natural number with at most R prime factors, counted with multiplicity.