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A194371 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) < 0, where r=sqrt(3) and fractional part is denoted by < >.

%I A194371 #14 Feb 15 2021 22:32:45
%S A194371 1,5,9,13,15,16,17,19,20,21,23,24,25,27,31,35,39,57,61,65,69,71,72,73,
%T A194371 75,76,77,79,80,81,83,87,91,95,113,117,121,125,127,128,129,131,132,
%U A194371 133,135,136,137,139,143,147,151,169,173,177,181,183,184,185,187
%N A194371 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) < 0, where r=sqrt(3) and fractional part is denoted by < >.
%C A194371 See A194368.
%H A194371 G. C. Greubel, <a href="/A194371/b194371.txt">Table of n, a(n) for n = 1..1000</a>
%t A194371 r = Sqrt[3]; c = 1/2;
%t A194371 x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
%t A194371 y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
%t A194371 t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 100}];
%t A194371 Flatten[Position[t1, 1]]  (* A194371 *)
%t A194371 t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 800}];
%t A194371 Flatten[Position[t2, 1]] (* A194372 *)
%t A194371 t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}];
%t A194371 Flatten[Position[t3, 1]] (* A194373 *)
%Y A194371 Cf. A194368.
%K A194371 nonn
%O A194371 1,2
%A A194371 _Clark Kimberling_, Aug 23 2011