A001959 -id:A001959 - cp's OEIS frontend

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

N. J. A. Sloane

See Connell (1959) for further information.

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).

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

Cf. A001954, A001958, A001959, A001964-A001968.

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

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

Edited by Hugo Pfoertner, Dec 27 2021

A001960 a(n) = floor((n+2/3)*(5+sqrt(13))/2); v-pile positions in the 3-Wythoff game.

Original entry on oeis.org

2, 7, 11, 15, 20, 24, 28, 32, 37, 41, 45, 50, 54, 58, 63, 67, 71, 76, 80, 84, 88, 93, 97, 101, 106, 110, 114, 119, 123, 127, 131, 136, 140, 144, 149, 153, 157, 162, 166, 170, 174, 179, 183, 187, 192, 196, 200, 205, 209, 213, 218, 222, 226, 230, 235, 239, 243, 248

Offset: 0

N. J. A. Sloane

nonn

3-Wythoff game, i=2, the v-pile positions in the Connell terminology. - R. J. Mathar, Feb 14 2011

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).

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.

Complement of A001957.

Cf. A001954, A001958, A001959, A001963-A001968.

Table[Floor[(n + 2/3)*(5 + Sqrt[13])/2], {n, 0, 100}] (* T. D. Noe, Aug 17 2012 *)

a(n) = floor((n+2/3)*(5+sqrt(13))/2). - R. J. Mathar, Feb 14 2011

New name from Hugo Pfoertner, Dec 27 2021

cp's OEIS Frontend

A001963 Winning positions in the u-pile of the 4-Wythoff game with i=1.

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