A206907 n+[nr/s]+[nt/s], where []=floor, r=1/3, s=sqrt(3), t=1/s.

1, 2, 4, 5, 6, 9, 10, 11, 13, 14, 16, 18, 19, 20, 22, 24, 25, 27, 28, 29, 32, 33, 34, 36, 37, 39, 41, 42, 43, 45, 46, 48, 50, 51, 52, 54, 56, 57, 59, 60, 61, 64, 65, 66, 68, 69, 71, 73, 74, 75, 77, 79, 80, 82, 83, 84, 86, 88, 89, 91, 92, 93, 96, 97, 98, 100, 101

Offset

1,2

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.

Links

Table of n, a(n) for n=1..67.

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 *)

Crossrefs

Cf. A206903.

Sequence in context: A050015 A153218 A063656 * A076354 A361936 A069470

Adjacent sequences: A206904 A206905 A206906 * A206908 A206909 A206910

Keyword

nonn

Author

Clark Kimberling, Feb 13 2012

Status

approved