A001957 u-pile positions in the 3-Wythoff game with i=1. (Formerly M2302 N0908)

0, 1, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23, 25, 26, 27, 29, 30, 31, 33, 34, 35, 36, 38, 39, 40, 42, 43, 44, 46, 47, 48, 49, 51, 52, 53, 55, 56, 57, 59, 60, 61, 62, 64, 65, 66, 68, 69, 70, 72, 73, 74, 75, 77, 78, 79, 81, 82, 83, 85, 86, 87

Offset

0,3

Comments

See Connell (1959) for further information.

The complement is A001960. - Omar E. Pol, Jan 06 2009

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.

Formula

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

Mathematica

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

Crossrefs

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

Sequence in context: A287727 A298606 A039095 * A184484 A253897 A100966

Adjacent sequences: A001954 A001955 A001956 * A001958 A001959 A001960

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Edited by N. J. A. Sloane, Dec 27 2021

Status

approved