Definition:Lower Wythoff Sequence
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Definition
The lower Wythoff sequence is the Beatty sequence on the golden section $\phi$.
It starts:
- $0, 1, 3, 4, 6, 8, 9, 11, 12, 14, 16, 17, 19, 21, \ldots$
This sequence is A000201 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) www.jstor.org/stable/2300153.
Their names originate from the fact that, in the form of Wythoff pairs, they form the winning combinations of Wythoff's game.
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
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $1 \cdotp 61803 \, 39887 \, 49894 \, 84820 \, 45868 \, 34365 \, 63811 \, 77203 \, 09179 \, 80576 \ldots$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $1 \cdotp 61803 \, 39887 \, 49894 \, 84820 \, 45868 \, 34365 \, 63811 \, 77203 \, 09179 \, 80576 \ldots$
- Weisstein, Eric W. "Beatty Sequence." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BeattySequence.html