A206903 n+[ns/r]+[nt/r], where []=floor, r=3, s=sqrt(3), t=1/s.

1, 3, 4, 6, 7, 10, 12, 13, 15, 16, 19, 20, 22, 24, 25, 28, 29, 31, 32, 34, 37, 38, 40, 41, 43, 46, 47, 49, 50, 52, 53, 56, 58, 59, 61, 62, 65, 66, 68, 70, 71, 74, 75, 77, 78, 80, 83, 84, 86, 87, 89, 92, 93, 95, 96, 98, 99, 102, 104, 105, 107, 108, 111, 112, 114

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. A206904, A206905.

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 *)