A001961 A Beatty sequence: floor(n * (sqrt(5) - 1)). (Formerly M0540 N0192)

1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23, 24, 25, 27, 28, 29, 30, 32, 33, 34, 35, 37, 38, 39, 40, 42, 43, 44, 45, 46, 48, 49, 50, 51, 53, 54, 55, 56, 58, 59, 60, 61, 63, 64, 65, 66, 67, 69, 70, 71, 72, 74, 75, 76, 77, 79, 80, 81, 82, 84

Offset

1,2

Comments

u-pile positions of the 4-Wythoff game with parameter i=0 (Connell nomenclature). - R. J. Mathar, Feb 14 2011

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 = 1..10000

Ian G. Connell, A generalization of Wythoff's game, Canad. Math. Bull. 2 (1959) 181-190.

A. S. Fraenkel, How to beat your Wythoff games' opponent on three fronts, Amer. Math. Monthly, 89 (1982), 353-361 (the case a=4).

Wen An Liu and Xiao Zhao, Adjoining to (s,t)-Wythoff's game its P-positions as moves, Discrete Applied Mathematics 179 (2014) 28-43. See Table 1.

N. J. A. Sloane, Families of Essentially Identical Sequences, Mar 24 2021 (Includes this sequence)

Index entries for sequences related to Beatty sequences

Formula

a(n) = A005206(2*n-1). - Peter Bala, Aug 09 2022

Mathematica

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

Crossrefs

Complement of A001962. Cf. A001965, A005206.

Sequence in context: A115180 A045774 A045681 * A020656 A358849 A039116

Adjacent sequences: A001958 A001959 A001960 * A001962 A001963 A001964

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Missing right parenthesis in description corrected May 15 1995

Status

approved