CONSECUTIVE SQUARE-FREE NUMBERS IN PIATETSKI-SHAPIRO SEQUENCES
Pinthira Tangsupphathawat, Teerapat Srichan, Vichian Laohakosol · Bulletin of the Australian Mathematical Society · 2021
Abstract Using a method due to Rieger [‘Remark on a paper of Stux concerning squarefree numbers in non-linear sequences’, Pacific J. Math.78(1) (1978), 241–242], we prove that the Piatetski-Shapiro sequence defined by $\{\lfloor n^c \rfloor : n\in \mathbb {N}\}$ contains infinitely many consecutive square-free integers whenever $1 .