%I #9 Feb 14 2021 21:40:18

%S 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 48,49,50,52,53,54,55,56,57,59,60,62,65,66,67,69,70,71,72,73,74,76,77,

%U 78,79,80,81,82,83,84,85,86,87,88,89,90,91,93,94,95,96,97,98

%N 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 See A194368.

%t r = Sqrt[2]; c = 1/r;

%t x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]

%t y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]

%t t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 200}];

%t Flatten[Position[t1, 1]] (* A184465 *)

%t t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 200}];

%t Flatten[Position[t3, 1]] (* A184466 *)

%Y Cf. A194368.

%K nonn

%O 1,2

%A _Clark Kimberling_, Aug 24 2011