Beatty Sequences for a Quadratic Irrational: Decidability and
Applications
Beatty Sequences for a Quadratic Irrational: Decidability and
Applications
Let $\alpha$ and $\beta$ belong to the same quadratic field. We show that the inhomogeneous Beatty sequence $(\lfloor n \alpha + \beta \rfloor)_{n \geq 1}$ is synchronized, in the sense that there is a finite automaton that takes as input the Ostrowski representations of $n$ and $y$ in parallel, and …