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A194403 (A194402)/2.

%I A194403 #5 Mar 30 2012 18:57:43
%S A194403 1,2,3,4,5,6,7,8,9,10,13,14,17,18,19,20,21,22,23,24,25,26,27,30,31,34,
%T A194403 35,36,37,38,39,40,41,42,43,44,45,46,49,50,53,54,55,56,57,58,59,60,61,
%U A194403 62,63,66,67,70,71,72,73,74,75,76,77,78,79,80,81,82,85,86,89
%N A194403 (A194402)/2.
%C A194403 See A194368.
%t A194403 r = GoldenRatio; c = 1/2;
%t A194403 x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
%t A194403 y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
%t A194403 t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 200}];
%t A194403 Flatten[Position[t1, 1]]       (* A194401 *)
%t A194403 t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 200}];
%t A194403 Flatten[Position[t2, 1]]       (* A194402 *)
%t A194403 %/2                            (* A194403 *)
%t A194403 t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 200}];
%t A194403 Flatten[Position[t3, 1]]       (* A194404 *)
%Y A194403 Cf. A194368.
%K A194403 nonn
%O A194403 1,2
%A A194403 _Clark Kimberling_, Aug 24 2011