A001959 u-pile numbers for the 3-Wythoff game with i=2.

0, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 15, 16, 17, 19, 20, 21, 23, 24, 25, 26, 28, 29, 30, 32, 33, 34, 36, 37, 38, 39, 41, 42, 43, 45, 46, 47, 49, 50, 51, 52, 54, 55, 56, 58, 59, 60, 62, 63, 64, 66, 67, 68, 69, 71, 72, 73, 75, 76, 77, 79, 80, 81, 82, 84, 85, 86, 88

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

See Connell (1959) for further information.

References

• 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

Crossrefs

Cf. A001954, A001958, A001960, A001963-A001968.

Programs

Mathematica

Table[Floor[(n + 2/3)*(Sqrt[13] - 1)/2], {n, 0, 100}] (* T. D. Noe, Aug 17 2012 *)

Formula

a(n) = floor( (n+2/3)*(sqrt(13)-1)/2 ). - R. J. Mathar, Feb 14 2011

Extensions

Edited by Hugo Pfoertner, Dec 27 2021