Definition
A positive irrational number generates the Beatty sequence
If then is also a positive irrational number. They naturally satisfy
and the sequences
- and
form a pair of complementary Beatty sequences.
A more general non-homogeneous Beatty sequence takes the form
where is a real number. For, the complementary non-homogeneous Beatty sequences can be found by making so that
- and
form a pair of complementary Beatty sequences. For other values of the procedure for finding complementary sequences is not as straightforward.
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