OEIS A00210: Beatty sequences floor(n(e−1)) and Rayleigh's complementary partition

Explore A00210, the Beatty sequence floor(n(e−1)). We explain Rayleigh's theorem: with R = e−1 and S = R/(R−1), the two Beatty sequences partition the positive integers, revealing deep connections to discrepancy, Sturmian sequences, and modular patterns like A082977. We also touch on generalizations (Espensky's theorem), practical Maple/Mathematica formulas from the OEIS entry, and pointers to further reading, including Connell's work on BD sequences.

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