A206908 a(n) = 4*n + floor(n/sqrt(3)).

4, 9, 13, 18, 22, 27, 32, 36, 41, 45, 50, 54, 59, 64, 68, 73, 77, 82, 86, 91, 96, 100, 105, 109, 114, 119, 123, 128, 132, 137, 141, 146, 151, 155, 160, 164, 169, 173, 178, 183, 187, 192, 196, 201, 205, 210, 215, 219, 224, 228, 233, 238, 242, 247, 251

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.

Original name:

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A206903.

Programs

Maple

seq(4*n+floor(n/sqrt(3)),n=1..100); # Robert Israel, Oct 18 2020

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 *)

Extensions

Name changed by Robert Israel, Oct 18 2020