@article{Qi2022, 
author = {Jinyun Qi and Zhefeng Xu},
title = {Almost primes in generalized Piatetski-Shapiro sequences},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {8},
pages = {14154-14162},
keywords = {Piatetski-Shapiro sequences, almost primes, exponent pair},
url = {https://www.sciopen.com/article/10.3934/math.2022780},
doi = {10.3934/math.2022780},
abstract = {We consider a generalization of Piatetski-Shapiro sequences in the sense of Beatty sequences, which is of the form              (              ⌊                  α                      n            c                    +          β                ⌋            )              n      =      1              ∞       with real numbers    α      ⩾    1  ,  c  >  1 and    β.In this paper, we prove that there are infinitely many    R-almost primes in sequences              (              ⌊        α                  n          c                +        β        ⌋            )              n      =      1              ∞       if    c  ∈  (  1  ,      c    R    ) and        c    R   is an explicit constant depending on    R.}
}