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A045681 Extension of Beatty sequence; complement of A045682.

%I A045681 #20 Feb 12 2014 18:15:47
%S A045681 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 A045681 31,33,34,35,36,38,39,40,41,43,44,45,46,47,48,50,51,52,53,55,56,57,58,
%U A045681 60,61,62,63,65,66,67,68,69,70,72,73
%N A045681 Extension of Beatty sequence; complement of A045682.
%C A045681 (s,t)-sequences; the case s=2, t=3.
%D A045681 Clark Kimberling, Complementary Equations, Journal of Integer Sequences, Vol. 10 (2007), Article 07.1.4.
%H A045681 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 A045681 <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>
%F A045681 a(n)=mex {a(i), b(i):0<=i<n}, where b=A045682, mex S=least integer >= 0 not in the sequence S.
%t A045681 s=2; t=3;
%t A045681 mex:=First[Complement[Range[1,Max[#1]+1],#1]]&;
%t A045681 a[0]=0; b[n_]:=b[n]=s*a[n]+t*n;
%t A045681 a[n_]:=a[n]=mex[Flatten[Table[{a[i],b[i]},{i,0,n-1}]]];
%t A045681 Table[a[n],{n,200}] (* A045681 *)
%t A045681 Table[b[n],{n,200}] (* A045682 *)
%t A045681 (* From _Clark Kimberling_, Apr 02 2011 *)
%Y A045681 Cf. A045671, A045672.
%K A045681 nonn
%O A045681 0,3
%A A045681 _Aviezri S. Fraenkel_