Articles containing proofs | Theorems in number theory | Diophantine approximation | Combinatorics on words | Integer sequences

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 a positive irrational number. 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. (Wikipedia).

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Related pages

Multiple (mathematics) | Square root of 2 | Sturmian word | Complement (set theory) | Irrational number | Mathematics | Lambek–Moser theorem | Integer | Partition of a set | Rational number | Alexander Bogomolny | Set (mathematics) | Wythoff array | Sequence | Wythoff's game | Golden ratio | John William Strutt, 3rd Baron Rayleigh | Floor and ceiling functions