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A194413 (A194412)/3.

%I A194413 #8 Nov 30 2017 18:22:09
%S A194413 1,3,4,5,7,8,9,11,12,13,14,15,16,17,18,19,20,21,22,23,25,26,27,29,30,
%T A194413 31,33,34,36,37,38,40,41,42,44,45,46,47,48,49,50,51,52,53,54,55,56,57,
%U A194413 61,65,69,70,71,73,74,75,77,78,79,80,81,82,83,84,85,86,87,88,89
%N A194413 (A194412)/3.
%C A194413 See A194368.
%H A194413 G. C. Greubel, <a href="/A194413/b194413.txt">Table of n, a(n) for n = 1..1000</a>
%t A194413 r = Sqrt[2]; c = 1/3;
%t A194413 x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
%t A194413 y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
%t A194413 t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 200}];
%t A194413 Flatten[Position[t1, 1]]         (* A194411 *)
%t A194413 t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 400}];
%t A194413 Flatten[Position[t2, 1]]         (* A194412 *)
%t A194413 %/3                              (* A194413 *)
%t A194413 t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 150}];
%t A194413 Flatten[Position[t3, 1]]         (* A194414 *)
%Y A194413 Cf. A194368, A194412.
%K A194413 nonn
%O A194413 1,2
%A A194413 _Clark Kimberling_, Aug 24 2011