Definition:Beatty Sequence
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Definition
Let $x$ be an irrational number.
The Beatty sequence on $x$ is the integer sequence $\BB_x$ defined as:
- $\BB_x := \sequence{\floor{n x} }_{n \mathop \in \Z_{\ge 0} }$
That is, the terms are the floors of the successive integer multiples of $x$.
Complementary Beatty Sequence
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 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
Source of Name
This entry was named for Samuel Beatty.
Sources
- Weisstein, Eric W. "Beatty Sequence." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BeattySequence.html