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A194382 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) = 0, where r=sqrt(8) and < > denotes fractional part.

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