Beatty sequence

In mathematics, a Beatty sequence (or homogeneous Beatty sequence) is the sequence of integers found by taking the floor of the positive multiples of an irrational number that is greater than one. Beatty sequences are named after Samuel Beatty, who wrote about them in 1926.

Rayleigh's theorem, named after Lord Rayleigh, states that the complement of a Beatty sequence, consisting of the positive integers that are not in the sequence, is itself a Beatty sequence generated by a different irrational number.

Beatty sequences can also be used to generate Sturmian words.

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