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A194380 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) > 0, where r=sqrt(7) and < > denotes fractional part.

%I A194380 #10 Feb 15 2021 02:20:29
%S A194380 31,33,45,47,79,81,93,95,127,129,141,143,175,177,189,191,223,225,237,
%T A194380 239,525,527,539,541,573,575,587,589,621,623,635,637,669,671,683,685,
%U A194380 717,719,731,733
%N A194380 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) > 0, where r=sqrt(7) and < > denotes fractional part.
%C A194380 See A194368.
%t A194380 r = Sqrt[7]; c = 1/2;
%t A194380 x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
%t A194380 y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
%t A194380 t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 100}];
%t A194380 Flatten[Position[t1, 1]]   (* A194378 *)
%t A194380 t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];
%t A194380 Flatten[Position[t2, 1]]  (* A194379 *)
%t A194380 t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 800}];
%t A194380 Flatten[Position[t3, 1]]   (* A194380 *)
%Y A194380 Cf. A194368, A194378, A194379.
%K A194380 nonn
%O A194380 1,1
%A A194380 _Clark Kimberling_, Aug 23 2011