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%I #20 Feb 12 2014 18:15:47
%S 0,1,2,3,4,6,7,8,9,11,12,13,14,16,17,18,19,21,22,23,24,25,26,28,29,30,
%T 31,33,34,35,36,38,39,40,41,43,44,45,46,47,48,50,51,52,53,55,56,57,58,
%U 60,61,62,63,65,66,67,68,69,70,72,73
%N Extension of Beatty sequence; complement of A045682.
%C (s,t)-sequences; the case s=2, t=3.
%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 <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>
%F a(n)=mex {a(i), b(i):0<=i<n}, where b=A045682, mex S=least integer >= 0 not in the sequence S.
%t s=2; t=3;
%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}] (* A045681 *)
%t Table[b[n],{n,200}] (* A045682 *)
%t (* From _Clark Kimberling_, Apr 02 2011 *)
%Y Cf. A045671, A045672.
%K nonn
%O 0,3
%A _Aviezri S. Fraenkel_
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