A001962 A Beatty sequence: floor(n * (sqrt(5) + 3)). (Formerly M3795 N1548)

5, 10, 15, 20, 26, 31, 36, 41, 47, 52, 57, 62, 68, 73, 78, 83, 89, 94, 99, 104, 109, 115, 120, 125, 130, 136, 141, 146, 151, 157, 162, 167, 172, 178, 183, 188, 193, 198, 204, 209, 214, 219, 225, 230, 235, 240, 246, 251, 256, 261, 267, 272, 277, 282, 287

Offset

1,1

Comments

Winning positions in the 4-Wythoff game, v-pile and parameter i=0 in the Connell nomenclature.

Note that sqrt(5)+3 = 2*phi^2, where phi=(1+sqrt(5))/2 is the golden ratio. [Gary Detlefs, Mar 30 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

Mathematica

With[{c=Sqrt[5]+3}, Floor[c Range[50]]] (* Harvey P. Dale, Mar 13 2011 *)

Prog

(Python)
from sympy import integer_nthroot
def A001962(n): return 3*n+integer_nthroot(5*n**2, 2)[0] # Chai Wah Wu, Mar 16 2021

Crossrefs

Complement of A001961.

A bisection of A001950.

Sequence in context: A313745 A028435 A313746 * A313747 A313748 A313749

Adjacent sequences: A001959 A001960 A001961 * A001963 A001964 A001965

Keyword

nonn

Author

N. J. A. Sloane

Status

approved