%I #8 Mar 30 2012 18:58:12

%S 7,15,23,30,38,47,55,62,70,78,87,94,102,110,117,126,134,142,149,157,

%T 166,174,181,189,197,206,213,221,229,236,245,253,261,268,276,285,293,

%U 300,308,316,325,332,340,348,355,364,372,380,387,395,404,412,419

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

%C 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.

%t r = 1/3; s = Sqrt[3]; t = 1/s;

%t a[n_] := n + Floor[n*s/r] + Floor[n*t/r];

%t b[n_] := n + Floor[n*r/s] + Floor[n*t/s];

%t c[n_] := n + Floor[n*r/t] + Floor[n*s/t];

%t Table[a[n], {n, 1, 70}] (* A206906 *)

%t Table[b[n], {n, 1, 80}] (* A206907 *)

%t Table[c[n], {n, 1, 70}] (* A206908 *)

%Y Cf. A206903.

%K nonn

%O 1,1

%A _Clark Kimberling_, Feb 13 2012