OEIS A000201: Lower Wythoff sequence

In this Deep Dive we unpack A000201—the lower Wythoff (Beatty) sequence. Defined by a(n) = floor(n·φ) with φ = (1 + √5)/2, it forms a companion pair with the upper Wythoff sequence b(n) = floor(n·φ²) (the “complementary” sequence). We explore how these two Beatty sequences partition the positive integers, why φ is the magic constant, and how the two lists up to infinity (1, 3, 4, 6, 8, …) and (2, 5, 7, 10, 13, …) interlock. We connect to Weishauf’s game: the losing positions are exactly the pairs (a(n), b(n)). Along the way, we touch on how these sequences relate to Sturmian words, and mention practical formulations (e.g., floor(n·φ)) and intuition behind the partition theorem of Beatty/Rayleigh. An episode for number theory fans who enjoy elegant partitions and game-theoretic links.

Note:  This podcast was AI-generated, and sometimes AI can make mistakes.  Please double-check any critical information.

Sponsored by Embersilk LLC