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A194465 Numbers m such that Sum_{k=1..m} ( - ) < 0, where r=sqrt(2) and c=sqrt(1/2), and < > denotes fractional part.

%I A194465 #9 Feb 14 2021 21:40:18
%S A194465 1,2,4,7,8,9,11,12,13,14,15,16,18,19,21,24,25,26,28,31,38,41,42,43,45,
%T A194465 48,49,50,52,53,54,55,56,57,59,60,62,65,66,67,69,70,71,72,73,74,76,77,
%U A194465 78,79,80,81,82,83,84,85,86,87,88,89,90,91,93,94,95,96,97,98
%N A194465 Numbers m such that Sum_{k=1..m} (<c + k*r> - <k*r>) < 0, where r=sqrt(2) and c=sqrt(1/2), and < > denotes fractional part.
%C A194465 See A194368.
%t A194465 r = Sqrt[2]; c = 1/r;
%t A194465 x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
%t A194465 y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
%t A194465 t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 200}];
%t A194465 Flatten[Position[t1, 1]]    (* A184465 *)
%t A194465 t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 200}];
%t A194465 Flatten[Position[t3, 1]]    (* A184466 *)
%Y A194465 Cf. A194368.
%K A194465 nonn
%O A194465 1,2
%A A194465 _Clark Kimberling_, Aug 24 2011