A045750 Extension of Beatty sequence, complement of A045749.

0, 4, 8, 12, 19, 23, 27, 34, 38, 42, 49, 53, 57, 61, 65, 69, 76, 80, 84, 91, 95, 99, 106, 110, 114, 118, 122, 126, 133, 137, 141, 148, 152, 156, 163, 167, 171, 175, 179, 183, 190, 194, 198, 205, 209, 213, 220, 224, 228, 235, 239, 243, 250, 254, 258

Offset: 0

Author

Aviezri S. Fraenkel

Keywords

• nonn

Comments

(s,t)-sequences; the case s=3, t=1.

Complement of A187749. It appears likely that A045750(n)=A187571(n) for all n>=1; the equation has been verified for n up to 500. - Clark Kimberling, Apr 02 2011

Links

• 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), #07.1.4.
• Index entries for sequences related to Beatty sequences

Crossrefs

Cf. A045671, A045672, A187571.

Programs

Mathematica

s=3; t=1;
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}] (* A045749 *)
Table[b[n], {n, 200}] (* A045750 *)
(* Clark Kimberling, Apr 02 2011 *)

Formula

a(n) = 3*A045749(n) + n.