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

0,2

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

Table of n, a(n) for n=0..54.

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

Formula

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

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 *)

Crossrefs

Cf. A045749, A045750.

Sequence in context: A313760 A313761 A045682 * A356106 A178892 A269805

Adjacent sequences: A045772 A045773 A045774 * A045776 A045777 A045778

Keyword

nonn

Author

Aviezri S. Fraenkel

Status

approved