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A194417 (A194416)/3.

%I A194417 #5 Mar 30 2012 18:57:43
%S A194417 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,21,22,23,26,27,28,31,32,
%T A194417 33,36,37,41,42,46,47,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,
%U A194417 67,68,69,72,73,74,77,78,79,82,83,84,87,88,92,93,97,98
%N A194417 (A194416)/3.
%C A194417 See A194368.
%t A194417 r = Sqrt[3]; c = 1/3;
%t A194417 x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
%t A194417 y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
%t A194417 t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 150}];
%t A194417 Flatten[Position[t1, 1]]           (* A194415 *)
%t A194417 t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];
%t A194417 Flatten[Position[t2, 1]]           (* A194416 *)
%t A194417 %/3                                (* A194417 *)
%t A194417 t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 500}];
%t A194417 Flatten[Position[t3, 1]]           (* A194418 *)
%Y A194417 Cf. A194368, A194416.
%K A194417 nonn
%O A194417 1,2
%A A194417 _Clark Kimberling_, Aug 24 2011