Almost Beatty Partitions

A. J. Hildebrand, Junxian Li, Xiaomin Li +1

Given $0<\alpha <1$, the Beatty sequence of density $\alpha$ is the sequence $B_{\alpha }=(\lfloor n/\alpha \rfloor {)}_{n\in \mathbb{N}}$. Beatty's theorem states that if $\alpha ,\beta$ are irrational numbers with $α+…