Definition:Upper Wythoff Sequence

Definition

Definition 1

The upper Wythoff sequence is the complementary Beatty sequence on the golden section $\phi$.

Definition 2

The upper Wythoff sequence is the Beatty sequence on the square $\phi^2$ of the golden section $\phi$.

The upper Wythoff sequence starts:

$0, 2, 5, 7, 10, 13, 15, 18, 20, 23, 26, 28, 31, 34, \ldots$

This sequence is A001950 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

Also see

• Equivalence of Definitions of Upper Wythoff Sequence

• Definition:Lower Wythoff Sequence

Source of Name

This entry was named for Willem Abraham Wythoff.

Sources

• 1926: Samuel Beatty: Problems for Solutions: 3173-3180 (Amer. Math. Monthly Vol. 33: p. 159)  www.jstor.org/stable/2300153

• 1927: Samuel Beatty: Solutions: 3177 (Amer. Math. Monthly Vol. 34: p. 159)  www.jstor.org/stable/2298716

• Weisstein, Eric W. "Beatty Sequence." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BeattySequence.html