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A194392 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) < 0, where r=sqrt(13) and < > denotes fractional part.

%I A194392 #10 Feb 15 2021 02:21:18
%S A194392 1,3,29,31,33,34,35,36,37,39,41,67,69,71,72,73,74,75,77,79,105,107,
%T A194392 143,145,181,183,209,211,213,214,215,216,217,219,221,247,249,251,252,
%U A194392 253,254,255,257,259,285,287,323,325,361,363,389,391,393,394,395
%N A194392 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) < 0, where r=sqrt(13) and < > denotes fractional part.
%C A194392 See A194368.
%t A194392 r = Sqrt[13]; c = 1/2;
%t A194392 x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
%t A194392 y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
%t A194392 t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 400}];
%t A194392 Flatten[Position[t1, 1]]       (* A194392 *)
%t A194392 t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];
%t A194392 Flatten[Position[t2, 1]]       (* A194393 *)
%t A194392 t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}];
%t A194392 Flatten[Position[t3, 1]]       (* A194394 *)
%Y A194392 Cf. A010470, A194368, A194393, A194394.
%K A194392 nonn
%O A194392 1,2
%A A194392 _Clark Kimberling_, Aug 23 2011