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A194424 (A194423)/3.

%I A194424 #11 Apr 03 2018 08:13:48
%S A194424 1,2,3,4,5,6,7,8,9,10,11,12,14,15,16,18,19,20,22,23,25,26,27,29,30,31,
%T A194424 33,34,35,36,37,38,39,40,41,42,43,44,45,47,48,49,51,52,53,55,56,57,61,
%U A194424 65,80,81,82,84,85,86,88,89,90,94,98
%N A194424 (A194423)/3.
%C A194424 See A194368.
%H A194424 G. C. Greubel, <a href="/A194424/b194424.txt">Table of n, a(n) for n = 1..2043</a>
%t A194424 r = Sqrt[2]; c = 2/3;
%t A194424 x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
%t A194424 y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
%t A194424 t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 300}];
%t A194424 Flatten[Position[t1, 1]]         (* A194422 *)
%t A194424 t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];
%t A194424 Flatten[Position[t2, 1]]         (* A194423 *)
%t A194424 %/3         (* A194424 *)
%t A194424 t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 300}];
%t A194424 Flatten[Position[t3, 1]]         (* A194425 *)
%Y A194424 Cf. A194368.
%K A194424 nonn
%O A194424 1,2
%A A194424 _Clark Kimberling_, Aug 24 2011