Beatty Sequences for a Quadratic Irrational: Decidability and Applications

Luke Schaeffer, Jeffrey Shallit, Stefan Zorcic

Let $\alpha$ and $\beta$ belong to the same quadratic field. We show that the inhomogeneous Beatty sequence $(\lfloor n\alpha +\beta \rfloor {)}_{n\ge 1}$ is synchronized, in the sense that there is…