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A206905 n+[nr/t]+[ns/t], where []=floor, r=3, s=sqrt(3), t=1/s.

%I A206905 #9 Mar 30 2012 18:58:12
%S A206905 9,18,27,36,45,55,64,73,82,91,101,110,119,128,137,147,156,165,174,183,
%T A206905 193,202,211,220,229,239,248,257,266,275,285,294,303,312,321,331,340,
%U A206905 349,358,367,377,386,395,404,413,423,432,441,450,459,469,478
%N A206905 n+[nr/t]+[ns/t], where []=floor, r=3, s=sqrt(3), t=1/s.
%C A206905 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.
%t A206905 r = 3; s = Sqrt[3]; t = 1/s;
%t A206905 a[n_] := n + Floor[n*s/r] + Floor[n*t/r];
%t A206905 b[n_] := n + Floor[n*r/s] + Floor[n*t/s];
%t A206905 c[n_] := n + Floor[n*r/t] + Floor[n*s/t];
%t A206905 Table[a[n], {n, 1, 70}]  (* A206903 *)
%t A206905 Table[b[n], {n, 1, 70}]  (* A206904 *)
%t A206905 Table[c[n], {n, 1, 70}]  (* A206905 *)
%Y A206905 Cf. A206903, A206904.
%K A206905 nonn
%O A206905 1,1
%A A206905 _Clark Kimberling_, Feb 13 2012