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A194376 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) = 0, where r=sqrt(6) and < > denotes fractional part.

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