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A194389 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) > 0, where r=sqrt(11) and < > denotes fractional part.

%I A194389 #10 Feb 15 2021 02:21:07
%S A194389 1,17,19,20,21,23,33,35,36,37,38,39,40,41,42,43,45,55,57,58,59,61,77,
%T A194389 79,80,81,83,93,95,96,97,98,99,100,101,102,103,105,115,117,118,119,
%U A194389 121,137,139,140,141,143,153,155,156,157,158,159,160,161,162,163
%N A194389 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) > 0, where r=sqrt(11) and < > denotes fractional part.
%C A194389 See A194368.
%t A194389 r = Sqrt[11]; c = 1/2;
%t A194389 x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
%t A194389 y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
%t A194389 t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 200}];
%t A194389 Flatten[Position[t1, 1]]     (* A194387 *)
%t A194389 t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 200}];
%t A194389 Flatten[Position[t2, 1]]     (* A194388 *)
%t A194389 t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 200}];
%t A194389 Flatten[Position[t3, 1]]     (* A194389 *)
%Y A194389 Cf. A010468, A194368, A194387, A194388.
%K A194389 nonn
%O A194389 1,2
%A A194389 _Clark Kimberling_, Aug 23 2011