%I #10 Feb 15 2021 02:20:37
%S 4,6,10,12,16,18,22,24,28,30,34,40,46,52,58,64,104,110,116,122,128,
%T 134,138,140,144,146,150,152,156,158,162,164,168,170,172,176,178,182,
%U 184,188,190,194,196,200,202,204,208,210,214,216,220,222,226,228
%N Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) = 0, where r=sqrt(8) and < > denotes fractional part.
%C See A194368.
%t r = Sqrt[8]; 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, 100}];
%t Flatten[Position[t1, 1]] (* A194381 *)
%t t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];
%t Flatten[Position[t2, 1]] (* A194382 *)
%t %/2 (* A194383 *)
%t t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 600}];
%t Flatten[Position[t3, 1]] (* A194384 *)
%Y Cf. A010466, A194368, A194383.
%K nonn
%O 1,1
%A _Clark Kimberling_, Aug 23 2011
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