Year: 2025
Type: article
Abstract: The Piatetski-Shapiro sequences are sequences of the form ( ⌊ n c ⌋ ) n = 1 ∞ {\left(\lfloor {n}^{c}\rfloor )}_{n=1}^{\infty } and the Beatty sequence is the sequence of integers ( ⌊ α n + β ⌋ ) n = 1 ∞ {(\lfloor \alpha n+\beta \rfloor )}_{n=1}^{\infty } . We prove that there are infinitely many Carmichael numbers composed of entirely the primes from the intersection of a Piatetski-Shapiro sequence and a Beatty sequence for c ∈ 1 , 19137 18746 c\in \left(\phantom{\rule[-0.75em]{}{0ex}},1,\frac{19137}{18746}\right) , α > 1 \alpha \gt 1 irrational and of finite type by investigating the Piatetski-Shapiro primes in arithmetic progressions in a Beatty sequence. Moreover, we also discuss the intersection of a Piatetski-Shapiro sequence and multiple Beatty sequences in arithmetic progressions.
Source: Open Mathematics
Authors: Jinyun Qi, Victor Zhenyu Guo
Institutions: Xi’an University, Xi'an Jiaotong University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,187
Awards: G1052736392, G6023350676
OpenAlex ID: W4410826446