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arXiv · 2211.10153

A generalization of Piatetski-Shapiro sequences (II)

Jinjiang Li·Jinyun Qi·Min Zhang
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Abstract

Suppose that $\alpha,\beta\in\mathbb{R}$. Let $\alpha\geqslant1$ and $c$ be a real number in the range $1<c< 12/11$. In this paper, it is proved that there exist infinitely many primes in the generalized Piatetski--Shapiro sequence, which is defined by $(\lfloor\alpha n^c+\beta\rfloor)_{n=1}^\infty$. Moreover, we also prove that there exist infinitely many Carmichael numbers composed entirely of primes from the generalized Piatetski--Shapiro sequences with $c\in(1,\frac{19137}{18746})$. The two theorems constitute improvements upon previous results by Guo and Qi.

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Jinjiang Li, Jinyun Qi, Min Zhang. 2022-11-18. A generalization of Piatetski-Shapiro sequences (II). https://arxiv.org/abs/2211.10153

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