# Definition:Beatty Sequence/Complementary

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## Definition

Let $x$ be an irrational number.

Let $\BB_x$ be the **Beatty sequence** on $x$.

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

## Also see

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

## Source of Name

This entry was named for Samuel Beatty.