A game played with two heaps of counters in which a player may take any number from either heap or the same number from both. The player taking the last counter wins.
The 
th safe combination
is 
, where 
, with 
the golden ratio and 
the floor
function. It is also true that 
. The first few safe
combinations are (1, 2), (3, 5), (4, 7), (6, 10), ... (OEIS A000201
and A001950), which are the pairs of elements
from the complementary Beatty sequences for 
and 
(Wells 1986, p. 40).
Wythoff's Game
See also
Beatty Sequence, Nim, SafeExplore with Wolfram|Alpha
References
Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, pp. 39-40, 1987.Coxeter, H. S. M. "The Golden Section, Phyllotaxis, and Wythoff's Game." Scripta Math. 19, 135-143, 1953.O'Beirne, T. H. Puzzles and Paradoxes. Oxford, England: Oxford University Press, pp. 109 and 134-138, 1965.Sloane, N. J. A. Sequences A000201/M2322 and A001950/M1332 in "The On-Line Encyclopedia of Integer Sequences."Wells, D. The Penguin Dictionary of Curious and Interesting Numbers. Middlesex, England: Penguin Books, p. 40, 1986.Wythoff, W. A. "A Modification of the Game of Nim." Nieuw Arch. Wisk. 8, 199-202, 1907/1909.Referenced on Wolfram|Alpha
Wythoff's GameCite this as:
Weisstein, Eric W. "Wythoff's Game." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/WythoffsGame.html