Examples
For r = the golden mean, we have s = r + 1. In this case, the sequence, known as the lower Wythoff sequence, is
- 1, 3, 4, 6, 8, 9, 11, 12, 14, 16, 17, 19, 21, 22, 24, 25, 27, 29, ... (sequence A000201 in OEIS).
and the complementary sequence, the upper Wythoff sequence, is
- 2, 5, 7, 10, 13, 15, 18, 20, 23, 26, 28, 31, 34, 36, 39, 41, 44, 47, ... (sequence A001950 in OEIS).
These sequences define the optimal strategy for Wythoff's game, and are used in the definition of the Wythoff array
As another example, for r = √2, we have s = 2 + √2. In this case, the sequences are
- 1, 2, 4, 5, 7, 8, 9, 11, 12, 14, 15, 16, 18, 19, 21, 22, 24, ... (sequence A001951 in OEIS) and
- 3, 6, 10, 13, 17, 20, 23, 27, 30, 34, 37, 40, 44, 47, 51, 54, 58, ... (sequence A001952 in OEIS).
Notice that any number in the first sequence is lacking in the second, and vice versa.
Read more about this topic: Beatty Sequence
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