Colloquium Mathematicum, vol.160, no.1, pp.53-63, 2020 (SCI-Expanded)
Let α and β be fixed real numbers and suppose that α > 1 is irrational and of finite type. We study values of the non-homogeneous Beatty sequence (Formula Presented) that are free of large prime factors, where (Formula Presented) is the largest integer not exceeding x.