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A045774 Extension of Beatty sequence; complement of A045775. 2


%S 0,1,2,3,4,6,7,8,9,11,12,13,14,16,17,18,19,21,22,23,24,25,26,27,29,30,

%T 31,32,34,35,36,37,39,40,41,42,44,45,46,47,48,49,50,52,53,54,55,57,58,

%U 59,60,62,63,64,65

%N Extension of Beatty sequence; complement of A045775.

%C (s,t)-sequences; the case s=3, t=2.

%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), 1-13.

%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, 179 (2014), 28-43. See Table 5.

%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=A045775, mex S=least integer >= 0 not in the sequence S.

%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 (* _Clark Kimberling_, Apr 02 2011 *)

%Y Cf. A045749, A045750.

%K nonn

%O 0,3

%A _Aviezri S. Fraenkel_

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Last modified April 25 16:08 EDT 2019. Contains 322461 sequences. (Running on oeis4.)