Definition:Upper Wythoff Sequence/Definition 2

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

It 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

Source of Name

This entry was named for Willem Abraham Wythoff.

Historical Note

The upper Wythoff sequence and lower Wythoff sequence were introduced in $1926$ by Samuel Beatty in a much-cited puzzle page: Problems for Solutions: 3173-3180 (Amer. Math. Monthly Vol. 33: p. 159)

Their names originate from the fact that, in the form of Wythoff pairs, they form the winning combinations of Wythoff's game.