%I #25 Sep 26 2018 09:50:53
%S 0,4,8,12,19,23,27,34,38,42,49,53,57,61,65,69,76,80,84,91,95,99,106,
%T 110,114,118,122,126,133,137,141,148,152,156,163,167,171,175,179,183,
%U 190,194,198,205,209,213,220,224,228,235,239,243,250,254,258
%N Extension of Beatty sequence, complement of A045749.
%C (s,t)-sequences; the case s=3, t=1.
%C Complement of A187749. It appears likely that A045750(n)=A187571(n) for all n>=1; the equation has been verified for n up to 500. - _Clark Kimberling_, Apr 02 2011
%H 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 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 <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>
%F a(n) = 3*A045749(n) + n.
%t s=3; t=1;
%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}] (* A045749 *)
%t Table[b[n], {n, 200}] (* A045750 *)
%t (* _Clark Kimberling_, Apr 02 2011 *)
%Y Cf. A045671, A045672, A187571.
%K nonn
%O 0,2
%A _Aviezri S. Fraenkel_