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Lower Wythoff sequence (a Beatty sequence): a(n) = floor(n*phi), where phi = (1+sqrt(5))/2 = A001622.
(history; published version)
#286 by Charles R Greathouse IV at Sun Feb 16 08:32:20 EST 2025
LINKS

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BeattySequence.html">Beatty Sequence</a>

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GoldenRatio.html">Golden Ratio</a>

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RabbitConstant.html">Rabbit Constant</a>

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/WythoffsGame.html">Wythoff's Game</a>

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/WythoffArray.html">Wythoff Array</a>

Discussion
Sun Feb 16
08:32
OEIS Server: https://oeis.org/edit/global/3014
#285 by Russ Cox at Sun Jan 05 19:51:31 EST 2025
LINKS

Peter G. Anderson, <a href="https://www.fq.math.ca/Papers1/58-5/anderson.pdf">The Fibonacci word as a 2-adic number and its continued fraction</a>, Fibonacci Quarterly (2020) Vol. 58, No. 5, 21-24.

L. Carlitz, Richard Scoville, and V. E. Hoggatt, Jr., <a href="https://www.fq.math.ca/Scanned/10-1/carlitz1.pdf">Fibonacci representations</a>, Fib. Quart., Vol. 10, No. 1 (1972), pp. 1-28.

L. Carlitz, R. Scoville, and T. Vaughan, <a href="https://www.fq.math.ca/Scanned/11-4/carlitz.pdf">Some arithmetic functions related to Fibonacci numbers</a>, Fib. Quart., 11 (1973), 337-386.

P. J. Downey and R. E. Griswold, <a href="https://www.fq.math.ca/Scanned/22-4/downey.pdf">On a family of nested recurrences</a>, Fib. Quart., 22 (1984), 310-317.

Clark Kimberling, <a href="https://www.fq.math.ca/Papers1/52-5/Problems.pdf">Problem Proposals</a>, The Fibonacci Quarterly, vol. 52 #5, 2015, p5-14.

Vincent Russo and Loren Schwiebert, <a href="https://www.fq.math.ca/49-2.html">Beatty Sequences, Fibonacci Numbers, and the Golden Ratio</a>, The Fibonacci Quarterly, Vol 49, Number 2, May 2011.

J. C. Turner, <a href="https://www.fq.math.ca/Scanned/27-1/turner.pdf">The alpha and the omega of the Wythoff pairs</a>, Fib. Q., 27 (1989), 76-86.

Discussion
Sun Jan 05
19:51
OEIS Server: https://oeis.org/edit/global/3012
#284 by Russ Cox at Sun Jan 05 19:24:35 EST 2025
LINKS

L. Carlitz, Richard Scoville, and V. E. Hoggatt, Jr., <a href="http://www.fq.math.ca/Scanned/10-1/carlitz1.pdf">Fibonacci representations</a>, Fib. Quart., Vol. 10, No. 1 (1972), pp. 1-28.

L. Carlitz, R. Scoville, and T. Vaughan, <a href="http://www.fq.math.ca/Scanned/11-4/carlitz.pdf">Some arithmetic functions related to Fibonacci numbers</a>, Fib. Quart., 11 (1973), 337-386.

P. J. Downey and R. E. Griswold, <a href="http://www.fq.math.ca/Scanned/22-4/downey.pdf">On a family of nested recurrences</a>, Fib. Quart., 22 (1984), 310-317.

Clark Kimberling, <a href="http://www.fq.math.ca/Papers1/52-5/Problems.pdf">Problem Proposals</a>, The Fibonacci Quarterly, vol. 52 #5, 2015, p5-14.

Vincent Russo and Loren Schwiebert, <a href="http://www.fq.math.ca/49-2.html">Beatty Sequences, Fibonacci Numbers, and the Golden Ratio</a>, The Fibonacci Quarterly, Vol 49, Number 2, May 2011.

J. C. Turner, <a href="http://www.fq.math.ca/Scanned/27-1/turner.pdf">The alpha and the omega of the Wythoff pairs</a>, Fib. Q., 27 (1989), 76-86.

Discussion
Sun Jan 05
19:24
OEIS Server: https://oeis.org/edit/global/3011
#283 by Michael De Vlieger at Sat Jun 01 12:02:08 EDT 2024
STATUS

reviewed

#282 by Stefano Spezia at Sat Jun 01 10:02:20 EDT 2024
STATUS

proposed

#281 by Joerg Arndt at Sat Jun 01 10:00:39 EDT 2024
STATUS

editing

Discussion
Sat Jun 01
10:01
Stefano Spezia: I apologize for the blank.
10:02
Stefano Spezia: Thanks
#280 by Joerg Arndt at Sat Jun 01 10:00:35 EDT 2024
LINKS

A. J. Macfarlane, <a href="https://arxiv.org/abs/2405.18128">On the fibbinary numbers and the Wythoffarray </a>, arXiv:2405.18128 [math.CO], 2024. See page 2.

STATUS

proposed

#279 by Michel Marcus at Sat Jun 01 09:52:45 EDT 2024
STATUS

editing

Discussion
Sat Jun 01
09:56
Stefano Spezia: Ok. Thanks
#278 by Michel Marcus at Sat Jun 01 09:52:37 EDT 2024
LINKS

N. Fox, <a href="http://arxiv.org/abs/1407.2823">On Aperiodic Subtraction Games with Bounded Nim Sequence</a>, arXiv preprint arXiv:1407.2823 [math.CO], 2014.

STATUS

proposed

Discussion
Sat Jun 01
09:52
Michel Marcus: oeis user
#277 by Stefano Spezia at Sat Jun 01 09:44:32 EDT 2024
STATUS

editing