A045775 Extension of Beatty sequence; complement of A045774.

0, 5, 10, 15, 20, 28, 33, 38, 43, 51, 56, 61, 66, 74, 79, 84, 89, 97, 102, 107, 112, 117, 122, 127, 135, 140, 145, 150, 158, 163, 168, 173, 181, 186, 191, 196, 204, 209, 214, 219, 224, 229, 234, 242, 247, 252, 257, 265, 270, 275, 280, 288, 293, 298, 303

Offset: 0

Author

Aviezri S. Fraenkel

Keywords

• nonn

Comments

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

References

• Clark Kimberling, Complementary Equations, Journal of Integer Sequences, Vol. 10 (2007), Article 07.1.4.

Links

• A. S. Fraenkel, Heap games, numeration systems and sequences, Annals of Combinatorics, 2 (1998), 197-210.
• Wen An Liu and Xiao Zhao, Adjoining to (s,t)-Wythoff's game its P-positions as moves, Discrete Applied Mathematics, 27 August 2014; see Table 5.
• Index entries for sequences related to Beatty sequences

Crossrefs

Cf. A045749, A045750.

Programs

Mathematica

s=3; t=2;
mex:=First[Complement[Range[1,Max[#1]+1],#1]]&;
a[0]=0; b[n_]:=b[n]=s*a[n]+t*n;
a[n_]:=a[n]=mex[Flatten[Table[{a[i],b[i]},{i,0,n-1}]]];
Table[a[n],{n,200}] (* A045774 *)
Table[b[n],{n,200}] (* A045775 *)
(* From Clark Kimberling, Apr 02 2011 *)

Formula

a(n) = 3*A045774(n)+2*n.