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A194395 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) < 0, where r=sqrt(14) and < > denotes fractional part.

%I A194395 #10 Feb 15 2021 02:18:42
%S A194395 1,5,9,13,17,21,25,29,31,32,33,35,36,37,39,40,41,43,44,45,47,48,49,51,
%T A194395 52,53,55,56,57,59,63,67,71,75,79,83,87,121,125,129,133,137,141,145,
%U A194395 149,151,152,153,155,156,157,159,160,161,163,164,165,167,168,169
%N A194395 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) < 0, where r=sqrt(14) and < > denotes fractional part.
%C A194395 See A194368.
%t A194395 r = Sqrt[14]; c = 1/2;
%t A194395 x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
%t A194395 y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
%t A194395 t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 200}];
%t A194395 Flatten[Position[t1, 1]]       (* A194395 *)
%t A194395 t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 200}];
%t A194395 Flatten[Position[t2, 1]]       (* A194396 *)
%t A194395 t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 300}];
%t A194395 Flatten[Position[t3, 1]]       (* A194397 *)
%Y A194395 Cf. A010471, A194368, A194396, A194397.
%K A194395 nonn
%O A194395 1,2
%A A194395 _Clark Kimberling_, Aug 23 2011