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

%I A206908 #11 Oct 18 2020 22:25:02
%S A206908 4,9,13,18,22,27,32,36,41,45,50,54,59,64,68,73,77,82,86,91,96,100,105,
%T A206908 109,114,119,123,128,132,137,141,146,151,155,160,164,169,173,178,183,
%U A206908 187,192,196,201,205,210,215,219,224,228,233,238,242,247,251
%N A206908 a(n) = 4*n + floor(n/sqrt(3)).
%C A206908 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.
%C A206908 Original name:
%C A206908 n+[nr/t]+[ns/t], where []=floor, r=1/3, s=sqrt(3), t=1/s.
%H A206908 Robert Israel, <a href="/A206908/b206908.txt">Table of n, a(n) for n = 1..10000</a>
%p A206908 seq(4*n+floor(n/sqrt(3)),n=1..100); # _Robert Israel_, Oct 18 2020
%t A206908 r = 1/3; s = Sqrt[3]; t = 1/s;
%t A206908 a[n_] := n + Floor[n*s/r] + Floor[n*t/r];
%t A206908 b[n_] := n + Floor[n*r/s] + Floor[n*t/s];
%t A206908 c[n_] := n + Floor[n*r/t] + Floor[n*s/t];
%t A206908 Table[a[n], {n, 1, 70}]  (* A206906 *)
%t A206908 Table[b[n], {n, 1, 80}]  (* A206907 *)
%t A206908 Table[c[n], {n, 1, 70}]  (* A206908 *)
%Y A206908 Cf. A206903.
%K A206908 nonn
%O A206908 1,1
%A A206908 _Clark Kimberling_, Feb 13 2012
%E A206908 Name changed by _Robert Israel_, Oct 18 2020