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- W3037913332 abstract "It is known that for all $alphain(1,2)$ and all integers $kge3$ and $rge1$, there exist infinitely many $ninmathbb{N}$ such that the sequence $(lfloor{(n+rj)^alpha}rfloor)_{j=0}^{k-1}$ is an arithmetic progression of length $k$. In this paper, we show that the asymptotic density of all the above $n$ is equal to $1/(k-1)$. Although the common difference $r$ is arbitrarily fixed in the above result, we also examine the case when $r$ is not fixed. Furthermore, we also examine the number of the above $n$ that are contained in a short interval." @default.
- W3037913332 created "2020-07-02" @default.
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- W3037913332 date "2020-06-24" @default.
- W3037913332 modified "2023-09-27" @default.
- W3037913332 title "Distributions of Arithmetic Progressions in Piatetski-Shapiro Sequence" @default.
- W3037913332 hasPublicationYear "2020" @default.
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