A045681 Extension of Beatty sequence; complement of A045682.

0, 1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 33, 34, 35, 36, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 55, 56, 57, 58, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 72, 73

Offset

0,3

Comments

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

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..60.

A. S. Fraenkel, Heap games, numeration systems and sequences, Annals of Combinatorics, 2 (1998), 197-210.

Index entries for sequences related to Beatty sequences

Formula

a(n)=mex {a(i), b(i):0<=i<n}, where b=A045682, mex S=least integer >= 0 not in the sequence S.

Mathematica

s=2; t=3;
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}] (* A045681 *)
Table[b[n], {n, 200}] (* A045682 *)
(* From Clark Kimberling, Apr 02 2011 *)

Crossrefs

Cf. A045671, A045672.

Sequence in context: A115180 A382744 A045774 * A001961 A020656 A358849

Adjacent sequences: A045678 A045679 A045680 * A045682 A045683 A045684

Keyword

nonn

Author

Aviezri S. Fraenkel

Status

approved