%I M3795 N1548 #54 Apr 29 2021 21:24:15
%S 5,10,15,20,26,31,36,41,47,52,57,62,68,73,78,83,89,94,99,104,109,115,
%T 120,125,130,136,141,146,151,157,162,167,172,178,183,188,193,198,204,
%U 209,214,219,225,230,235,240,246,251,256,261,267,272,277,282,287
%N A Beatty sequence: floor(n * (sqrt(5) + 3)).
%C Winning positions in the 4-Wythoff game, v-pile and parameter i=0 in the Connell nomenclature.
%C Note that sqrt(5)+3 = 2*phi^2, where phi=(1+sqrt(5))/2 is the golden ratio. [_Gary Detlefs_, Mar 30 2011]
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H T. D. Noe, <a href="/A001962/b001962.txt">Table of n, a(n) for n = 1..10000</a>
%H Ian G. Connell, <a href="http://dx.doi.org/10.4153/CMB-1959-024-3">A generalization of Wythoff's game</a>, Canad. Math. Bull. 2 (1959) 181-190.
%H A. S. Fraenkel, <a href="http://www.jstor.org/stable/2321643">How to beat your Wythoff games' opponent on three fronts</a>, Amer. Math. Monthly, 89 (1982), 353-361 (the case a=4).
%H Wen An Liu and Xiao Zhao, <a href="http://dx.doi.org/10.1016/j.dam.2014.08.009">Adjoining to (s,t)-Wythoff's game its P-positions as moves</a>, Discrete Applied Mathematics 179 (2014) 28-43. See Table 1.
%H N. J. A. Sloane, <a href="/A115004/a115004.txt">Families of Essentially Identical Sequences</a>, Mar 24 2021 (Includes this sequence)
%H <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>
%t With[{c=Sqrt[5]+3}, Floor[c Range[50]]] (* _Harvey P. Dale_, Mar 13 2011 *)
%o (Python)
%o from sympy import integer_nthroot
%o def A001962(n): return 3*n+integer_nthroot(5*n**2,2)[0] # _Chai Wah Wu_, Mar 16 2021
%Y Complement of A001961.
%Y A bisection of A001950.
%K nonn
%O 1,1
%A _N. J. A. Sloane_