A001963 Winning positions in the u-pile of the 4-Wythoff game with i=1.
0, 1, 2, 4, 5, 6, 7, 8, 10, 11, 12, 13, 15, 16, 17, 18, 20, 21, 22, 23, 25, 26, 27, 28, 29, 31, 32, 33, 34, 36, 37, 38, 39, 41, 42, 43, 44, 46, 47, 48, 49, 50, 52, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 65, 67, 68, 69, 70, 72, 73, 74, 75, 76, 78, 79, 80, 81, 83
Offset: 0
References
- N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Links
- T. D. Noe, Table of n, a(n) for n = 0..10000
- Ian G. Connell, A generalization of Wythoff's game, Canad. Math. Bull. 2 (1959) 181-190
Programs
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Mathematica
Table[Floor[(n + 1/4)*(Sqrt[5] - 1)], {n, 0, 100}] (* T. D. Noe, Aug 17 2012 *)
Formula
a(n) = floor( (n+1/4)*(sqrt(5)-1) ). - R. J. Mathar, Feb 14 2011
Extensions
Edited by Hugo Pfoertner, Dec 27 2021
Comments