Definition:Beatty Sequence/Complementary

Definition
Let $x$ be an irrational number. Let $\mathcal B_x$ be the Beatty sequence on $x$.

The complementary Beatty sequence on $x$ is the integer sequence formed by the integers which are missing from $\mathcal B_x$.

Also see

 * Beatty's Theorem, which proves that the complementary Beatty sequence on $x$ is a Beatty sequence on another irrational number $y$.