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A194388 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) = 0, where r=sqrt(11) and < > denotes fractional part.

%I A194388 #10 Feb 15 2021 02:21:03
%S A194388 2,4,14,16,18,22,24,26,30,32,34,44,46,48,52,54,56,60,62,64,74,76,78,
%T A194388 82,84,86,90,92,94,104,106,108,112,114,116,120,122,124,134,136,138,
%U A194388 142,144,146,150,152,154,164,166,168,172,174,176,180,182,184,194,196
%N A194388 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) = 0, where r=sqrt(11) and < > denotes fractional part.
%C A194388 Every term is even; see A194368.
%t A194388 r = Sqrt[11]; c = 1/2;
%t A194388 x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
%t A194388 y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
%t A194388 t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 200}];
%t A194388 Flatten[Position[t1, 1]]     (* A194387 *)
%t A194388 t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 200}];
%t A194388 Flatten[Position[t2, 1]]     (* A194388 *)
%t A194388 t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 200}];
%t A194388 Flatten[Position[t3, 1]]     (* A194389 *)
%Y A194388 Cf. A010468, A194368, A194387, A194389.
%K A194388 nonn
%O A194388 1,1
%A A194388 _Clark Kimberling_, Aug 23 2011