A045682 Extension of Beatty sequence; complement of A045681.

0, 5, 10, 15, 20, 27, 32, 37, 42, 49, 54, 59, 64, 71, 76, 81, 86, 93, 98, 103, 108, 113, 118, 125, 130, 135, 140, 147, 152, 157, 162, 169, 174, 179, 184, 191, 196, 201, 206, 211, 216, 223, 228, 233, 238, 245, 250, 255, 260, 267, 272, 277, 282, 289, 294, 299

Offset: 0

Author

Aviezri S. Fraenkel

Keywords

• nonn

Comments

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

Links

• A. S. Fraenkel, Heap games, numeration systems and sequences, Annals of Combinatorics, 2 (1998), 197-210.
• Index entries for sequences related to Beatty sequences

Crossrefs

Cf. A045671, A045672.

Programs

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 *)

Formula

a(n) = 2*A045681(n)+3*n.