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A194466 Numbers m such that Sum_{k=1..m} ( - ) > 0, where r=sqrt(2) and c=sqrt(1/2), and < > denotes fractional part.

%I A194466 #9 Feb 14 2021 20:51:33
%S A194466 3,5,6,10,17,20,22,23,27,29,30,32,33,34,35,36,37,39,40,44,46,47,51,58,
%T A194466 61,63,64,68,75,92,99,102,104,105,109,116,119,121,122,126,128,129,131,
%U A194466 132,133,134,135,136,138,139,143,145,146,150,157,160,162,163
%N A194466 Numbers m such that Sum_{k=1..m} (<c + k*r> - <k*r>) > 0, where r=sqrt(2) and c=sqrt(1/2), and < > denotes fractional part.
%C A194466 See A194368.
%t A194466 r = Sqrt[2]; c = 1/r;
%t A194466 x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
%t A194466 y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
%t A194466 t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 200}];
%t A194466 Flatten[Position[t1, 1]]    (* A184465 *)
%t A194466 t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 200}];
%t A194466 Flatten[Position[t3, 1]]    (* A184466 *)
%Y A194466 Cf. A194368.
%K A194466 nonn
%O A194466 1,1
%A A194466 _Clark Kimberling_, Aug 24 2011