A001967 u-pile positions for the 4-Wythoff game with i=3. (Formerly M0515 N0184)

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

0,2

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.

Formula

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

Mathematica

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

Crossrefs

Cf. A001968 (v-pile).

Sequence in context: A231004 A039161 A032797 * A226066 A005838 A184486

Adjacent sequences: A001964 A001965 A001966 * A001968 A001969 A001970

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Edited by Hugo Pfoertner, Dec 27 2021

Status

approved