@Inbook{Deshouillers2023,
author="Deshouillers, Jean-Marc
and Drmota, Michael
and M{\"u}llner, Clemens",
editor="Maier, Helmut
and Steuding, J{\"o}rn
and Steuding, Rasa",
title="Coprimality of Consecutive Elements in a Piatetski-Shapiro Sequence",
bookTitle="Number Theory in Memory of Eduard Wirsing",
year="2023",
publisher="Springer International Publishing",
address="Cham",
pages="91--98",
abstract="We show that in any Piatetski-Shapiro sequence ⌊nc⌋n{\$}{\$}{\backslash}left ({\backslash}lfloor n^c {\backslash}rfloor {\backslash}right ){\_}n{\$}{\$}with c in (1,+∞)∖ℕ{\$}{\$}(1, +{\backslash}infty ){\backslash}backslash {\backslash}mathbb {\{}N{\}}{\$}{\$}, there exist long subsequences of consecutive elements no pair of which are coprime, whereas for any c in (1,2){\$}{\$}(1, 2){\$}{\$}, there exist infinitely many n such that all the elements in {\{}⌊nc⌋,⌊(n+1)c⌋,{\ldots},⌊(n+H)c⌋{\}}{\$}{\$}{\backslash}{\{}{\backslash}lfloor n^c {\backslash}rfloor , {\backslash}lfloor (n+1)^c {\backslash}rfloor , {\backslash}ldots , {\backslash}lfloor (n+H)^c {\backslash}rfloor {\backslash}{\}}{\$}{\$}are pairwise coprime for H almost as large as min(c−1,1−c∕2)logn{\$}{\$}{\backslash}min (c-1,1-c/2){\backslash}log n{\$}{\$}.",
isbn="978-3-031-31617-3",
doi="10.1007/978-3-031-31617-3_7",
url="https://doi.org/10.1007/978-3-031-31617-3_7"
}