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)
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
KEYWORD
nonn
AUTHOR
STATUS
approved