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A194393 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) = 0, where r=sqrt(13) and < > denotes fractional part.

%I A194393 #10 Feb 15 2021 02:18:29
%S A194393 2,4,6,8,24,26,28,30,32,38,40,42,44,46,62,64,66,68,70,76,78,80,82,84,
%T A194393 100,102,104,106,108,110,112,138,140,142,144,146,148,150,176,178,180,
%U A194393 182,184,186,188,204,206,208,210,212,218,220,222,224,226,242,244
%N A194393 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) = 0, where r=sqrt(13) and < > denotes fractional part.
%C A194393 See A194368.
%t A194393 r = Sqrt[13]; c = 1/2;
%t A194393 x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
%t A194393 y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
%t A194393 t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 400}];
%t A194393 Flatten[Position[t1, 1]]       (* A194392 *)
%t A194393 t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];
%t A194393 Flatten[Position[t2, 1]]       (* A194393 *)
%t A194393 t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}];
%t A194393 Flatten[Position[t3, 1]]       (* A194394 *)
%Y A194393 Cf. A010470, A194368, A194392, A194394.
%K A194393 nonn
%O A194393 1,1
%A A194393 _Clark Kimberling_, Aug 23 2011