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A194468 Numbers m such that Sum_{k=1..m} ( - ) > 0, where r=sqrt(3) and c=sqrt(1/3), and < > denotes fractional part.

%I A194468 #8 Feb 14 2021 20:23:57
%S A194468 7,11,14,26,52,97,104,108,111,123,149,153,156,160,163,164,165,167,175,
%T A194468 179,182,194,201,205,208,220,317,362,369,373,376,388,414,582,679,724,
%U A194468 731,735,738,750,776
%N A194468 Numbers m such that Sum_{k=1..m} (<c + k*r> - <k*r>) > 0, where r=sqrt(3) and c=sqrt(1/3), and < > denotes fractional part.
%C A194468 See A194368.
%t A194468 Remove["Global`*"];
%t A194468 r = Sqrt[3]; c = 1/r;
%t A194468 x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
%t A194468 y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
%t A194468 t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 200}];
%t A194468 Flatten[Position[t1, 1]]    (* A184467 *)
%t A194468 t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 900}];
%t A194468 Flatten[Position[t3, 1]]    (* A184468 *)
%Y A194468 Cf. A194368.
%K A194468 nonn
%O A194468 1,1
%A A194468 _Clark Kimberling_, Aug 24 2011