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%I #10 Feb 15 2021 02:20:10
%S 2,4,6,8,20,22,24,26,28,40,42,44,46,48,60,62,64,66,68,80,82,84,86,88,
%T 198,200,202,204,206,218,220,222,224,226,238,240,242,244,246,258,260,
%U 262,264,266,278,280,282,284,286,396,398,400
%N Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) = 0, where r=sqrt(6) and < > denotes fractional part.
%C See A194368.
%t r = Sqrt[6]; c = 1/2;
%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, 500}];
%t Flatten[Position[t1, 1]] (* empty *)
%t t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 400}];
%t Flatten[Position[t2, 1]] (* A194376 *)
%t t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}];
%t Flatten[Position[t3, 1]] (* A194377 *)
%Y Cf. A194368, A194377.
%K nonn
%O 1,1
%A _Clark Kimberling_, Aug 23 2011
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