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A194467 Numbers m such that Sum_{k=1..m} ( - ) < 0, where r=sqrt(3) and c=sqrt(1/3), and < > denotes fractional part.

%I A194467 #9 Feb 14 2021 20:42:04
%S A194467 1,2,3,4,5,6,8,9,10,12,13,15,16,17,18,19,20,21,22,23,24,25,27,28,29,
%T A194467 30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,53,
%U A194467 54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74
%N A194467 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 A194467 See A194368.
%t A194467 Remove["Global`*"];
%t A194467 r = Sqrt[3]; c = 1/r;
%t A194467 x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
%t A194467 y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
%t A194467 t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 200}];
%t A194467 Flatten[Position[t1, 1]]    (* A184467 *)
%t A194467 t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 900}];
%t A194467 Flatten[Position[t3, 1]]    (* A184468 *)
%Y A194467 Cf. A194368.
%K A194467 nonn
%O A194467 1,2
%A A194467 _Clark Kimberling_, Aug 24 2011