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%I #19 Oct 25 2014 13:27:08
%S 0,5,10,15,20,28,33,38,43,51,56,61,66,74,79,84,89,97,102,107,112,117,
%T 122,127,135,140,145,150,158,163,168,173,181,186,191,196,204,209,214,
%U 219,224,229,234,242,247,252,257,265,270,275,280,288,293,298,303
%N Extension of Beatty sequence; complement of A045774.
%C (s,t)-sequences; the case s=3, t=2.
%D Clark Kimberling, Complementary Equations, Journal of Integer Sequences, Vol. 10 (2007), Article 07.1.4.
%H A. S. Fraenkel, <a href="http://arXiv.org/abs/math.CO/9809074">Heap games, numeration systems and sequences</a>, Annals of Combinatorics, 2 (1998), 197-210.
%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, 27 August 2014; see Table 5.
%H <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>
%F a(n) = 3*A045774(n)+2*n.
%t s=3; t=2;
%t mex:=First[Complement[Range[1,Max[#1]+1],#1]]&;
%t a[0]=0; b[n_]:=b[n]=s*a[n]+t*n;
%t a[n_]:=a[n]=mex[Flatten[Table[{a[i],b[i]},{i,0,n-1}]]];
%t Table[a[n],{n,200}] (* A045774 *)
%t Table[b[n],{n,200}] (* A045775 *)
%t (* From _Clark Kimberling_, Apr 02 2011 *)
%Y Cf. A045749, A045750.
%K nonn
%O 0,2
%A _Aviezri S. Fraenkel_
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