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A045749 Extension of Beatty sequence; complement of A045750.

%I A045749 #28 Sep 26 2018 09:50:45
%S A045749 0,1,2,3,5,6,7,9,10,11,13,14,15,16,17,18,20,21,22,24,25,26,28,29,30,
%T A045749 31,32,33,35,36,37,39,40,41,43,44,45,46,47,48,50,51,52,54,55,56,58,59,
%U A045749 60,62,63,64,66,67,68
%N A045749 Extension of Beatty sequence; complement of A045750.
%C A045749 (s,t)-sequences; the case s=3, t=1.
%C A045749 Complement of A045750.  It appears likely that A045749(n)=A187570(n) for all n>=1; the equation has been verified for n up to 500. - _Clark Kimberling_, Apr 02 2011
%H A045749 A. S. Fraenkel, <a href="https://arxiv.org/abs/math/9809074">Heap games, numeration systems and sequences</a>, arXiv:math/9809074 [math.CO], 1998; Annals of Combinatorics, 2 (1998), 197-210.
%H A045749 Clark Kimberling, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL10/Kimberling/kimberling26.html">Complementary equations</a>, J. Int. Seq. 19 (2007), #07.1.4.
%H A045749 <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>
%F A045749 a(n) = mex {a(i), b(i):0 <= i<n}, where b=A045750, mex S=least integer >= 0 not in the sequence S.
%t A045749 s=3; t=1;
%t A045749 mex:=First[Complement[Range[1,Max[#1]+1],#1]]&;
%t A045749 a[0]=0; b[n_]:=b[n]=s*a[n]+t*n;
%t A045749 a[n_]:=a[n]=mex[Flatten[Table[{a[i],b[i]},{i,0,n-1}]]];
%t A045749 Table[a[n],{n,200}] (* A045749 *)
%t A045749 Table[b[n],{n,200}] (* A045750 *)
%t A045749 (* _Clark Kimberling_, Apr 02 2011 *)
%Y A045749 Cf. A045681, A045682, A045749, A187570.
%K A045749 nonn
%O A045749 0,3
%A A045749 _Aviezri S. Fraenkel_