Definition:Beatty Sequence

Definition
Let $x$ be an irrational number.

The Beatty sequence on $x$ is the integer sequence $\mathcal B_x$ defined as:
 * $\mathcal B_x := \left\langle{\left\lfloor{n x}\right\rfloor}\right\rangle_{n \mathop \in \Z_{\ge 0} }$

That is, the terms are the floors of the successive integer multiples of $x$.

Also known as
A Beatty sequence is also known as a homogeneous Beatty sequence, to distinguish it specifically from a non-homogeneous Beatty sequence

Also see

 * Beatty's Theorem


 * Definition:Non-Homogeneous Beatty Sequence


 * Definition:Lower Wythoff Sequence
 * Definition:Upper Wythoff Sequence