A note on values of Beatty sequences that are free of large prime factors
Volume 160 / 2020
Colloquium Mathematicum 160 (2020), 53-63
MSC: Primary 11N25; Secondary 11L03.
DOI: 10.4064/cm7715-2-2019
Published online: 13 December 2019
Abstract
Let $\alpha $ and $\beta $ be fixed real numbers and suppose that $\alpha \gt 1$ is irrational and of finite type. We study values of the non-homogeneous Beatty sequence $ \def\fl#1{\lfloor#1\rfloor}\{ \fl {\alpha n +\beta }\}_{n=1}^{\infty }$ that are free of large prime factors, where $ \def\fl#1{\lfloor#1\rfloor}\fl {x}$ is the largest integer not exceeding $x$.
