A206905 n+[nr/t]+[ns/t], where []=floor, r=3, s=sqrt(3), t=1/s.

9, 18, 27, 36, 45, 55, 64, 73, 82, 91, 101, 110, 119, 128, 137, 147, 156, 165, 174, 183, 193, 202, 211, 220, 229, 239, 248, 257, 266, 275, 285, 294, 303, 312, 321, 331, 340, 349, 358, 367, 377, 386, 395, 404, 413, 423, 432, 441, 450, 459, 469, 478

Offset: 1

Author

Clark Kimberling, Feb 13 2012

Keywords

• nonn

Comments

The sequences A206903, A206904, A206905 partition the positive integers. To generate them, jointly rank the sets {n/3}, {n/sqrt(3)}, {n*sqrt(3)} for n>=1. The positions of n/3 in the joint ranking form A206903, and likewise for the other sequences.

Crossrefs

Cf. A206903, A206904.

Programs

Mathematica

r = 3; s = Sqrt[3]; t = 1/s;
a[n_] := n + Floor[n*s/r] + Floor[n*t/r];
b[n_] := n + Floor[n*r/s] + Floor[n*t/s];
c[n_] := n + Floor[n*r/t] + Floor[n*s/t];
Table[a[n], {n, 1, 70}]  (* A206903 *)
Table[b[n], {n, 1, 70}]  (* A206904 *)
Table[c[n], {n, 1, 70}]  (* A206905 *)