A206906 n+[ns/r]+[nt/r], where []=floor, r=1/3, s=sqrt(3), t=1/s.

7, 15, 23, 30, 38, 47, 55, 62, 70, 78, 87, 94, 102, 110, 117, 126, 134, 142, 149, 157, 166, 174, 181, 189, 197, 206, 213, 221, 229, 236, 245, 253, 261, 268, 276, 285, 293, 300, 308, 316, 325, 332, 340, 348, 355, 364, 372, 380, 387, 395, 404, 412, 419

Offset: 1

Author

Clark Kimberling, Feb 13 2012

Keywords

• nonn

Comments

The sequences A206906, A206907, A206908 partition the positive integers. To generate them, jointly rank the sets {3n}, {n/sqrt(3)}, {n*sqrt(3)} for n>=1. The positions of 3n in the joint ranking form A206906, and likewise for the other sequences.

Crossrefs

Cf. A206903.

Programs

Mathematica

r = 1/3; 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}]  (* A206906 *)
Table[b[n], {n, 1, 80}]  (* A206907 *)
Table[c[n], {n, 1, 70}]  (* A206908 *)