A001967 u-pile positions for the 4-Wythoff game with i=3.

0, 2, 3, 4, 5, 7, 8, 9, 10, 12, 13, 14, 15, 16, 18, 19, 20, 21, 23, 24, 25, 26, 28, 29, 30, 31, 33, 34, 35, 36, 38, 39, 40, 41, 42, 44, 45, 46, 47, 49, 50, 51, 52, 54, 55, 56, 57, 59, 60, 61, 62, 63, 65, 66, 67, 68, 70, 71, 72, 73, 75, 76, 77, 78, 80, 81, 82, 83

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

See Connell (1959) for further information.

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.

Crossrefs

Cf. A001968 (v-pile).

Programs

Mathematica

Table[Floor[(n + 3/4)*(Sqrt[5] - 1)], {n, 0, 100}] (* T. D. Noe, Aug 17 2012 *)

Formula

a(n) = floor( (n+3/4)*(sqrt(5)-1) ). - R. J. Mathar, Feb 14 2011

Extensions

Edited by Hugo Pfoertner, Dec 27 2021