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A194394 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) > 0, where r=sqrt(13) and < > denotes fractional part.

%I A194394 #10 Feb 15 2021 02:18:37
%S A194394 5,7,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,25,27,43,45,47,48,49,
%T A194394 50,51,52,53,54,55,56,57,58,59,60,61,63,65,81,83,85,86,87,88,89,90,91,
%U A194394 92,93,94,95,96,97,98,99,101,103,109,111,113,114,115,116,117
%N A194394 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) > 0, where r=sqrt(13) and < > denotes fractional part.
%C A194394 See A194368.
%t A194394 r = Sqrt[13]; c = 1/2;
%t A194394 x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
%t A194394 y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
%t A194394 t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 400}];
%t A194394 Flatten[Position[t1, 1]]       (* A194392 *)
%t A194394 t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];
%t A194394 Flatten[Position[t2, 1]]       (* A194393 *)
%t A194394 t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}];
%t A194394 Flatten[Position[t3, 1]]       (* A194394 *)
%Y A194394 Cf. A010470, A194368, A194392, A194393.
%K A194394 nonn
%O A194394 1,1
%A A194394 _Clark Kimberling_, Aug 23 2011