A045774 Extension of Beatty sequence; complement of A045775.

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, 31, 32, 34, 35, 36, 37, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 65

Offset

0,3

Comments

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

Links

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

A. S. Fraenkel, Heap games, numeration systems and sequences, arXiv:math/9809074 [math.CO], 1998; Annals of Combinatorics, 2 (1998), 197-210.

Clark Kimberling, Complementary equations, J. Int. Seq. 19 (2007), 1-13.

Wen An Liu and Xiao Zhao, Adjoining to (s,t)-Wythoff's game its P-positions as moves, Discrete Applied Mathematics, 179 (2014), 28-43. See Table 5.

Index entries for sequences related to Beatty sequences

Formula

a(n)=mex {a(i), b(i):0 <= i<n}, where b=A045775, mex S=least integer >= 0 not in the sequence S.

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 *)
(* Clark Kimberling, Apr 02 2011 *)

Crossrefs

Cf. A045749, A045750.

Sequence in context: A039199 A172269 A115180 * A045681 A001961 A020656

Adjacent sequences: A045771 A045772 A045773 * A045775 A045776 A045777

Keyword

nonn

Author

Aviezri S. Fraenkel

Status

approved