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A194378 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) < 0, where r=sqrt(7) and < > denotes fractional part.

%I A194378 #10 Feb 15 2021 02:20:25
%S A194378 1,3,4,5,6,7,8,9,10,11,12,13,15,17,18,19,20,21,22,23,24,25,26,27,29,
%T A194378 35,37,38,39,40,41,43,49,51,52,53,54,55,56,57,58,59,60,61,63,65,66,67,
%U A194378 68,69,70,71,72,73,74,75,77,83,85,86,87,88,89,91,97,99,100
%N A194378 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) < 0, where r=sqrt(7) and < > denotes fractional part.
%C A194378 See A194368.
%t A194378 r = Sqrt[7]; c = 1/2;
%t A194378 x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
%t A194378 y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
%t A194378 t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 100}];
%t A194378 Flatten[Position[t1, 1]]   (* A194378 *)
%t A194378 t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];
%t A194378 Flatten[Position[t2, 1]]  (* A194379 *)
%t A194378 t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 800}];
%t A194378 Flatten[Position[t3, 1]]   (* A194380 *)
%Y A194378 Cf. A194368, A194379, A194380.
%K A194378 nonn
%O A194378 1,2
%A A194378 _Clark Kimberling_, Aug 23 2011