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%I #8 Mar 30 2012 18:58:12
%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,
%T 39,41,42,43,45,46,48,50,51,52,54,56,57,59,60,61,64,65,66,68,69,71,73,
%U 74,75,77,79,80,82,83,84,86,88,89,91,92,93,96,97,98,100,101
%N n+[nr/s]+[nt/s], 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 1,2
%A _Clark Kimberling_, Feb 13 2012
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