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A194384 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) > 0, where r=sqrt(8) and < > denotes fractional part.

%I A194384 #10 Feb 15 2021 02:20:41
%S A194384 5,11,17,23,29,139,145,151,157,163,169,173,174,175,179,180,181,185,
%T A194384 186,187,191,192,193,197,198,199,203,209,215,221,227,233,343,349,355,
%U A194384 361,367,373,377,378,379,383,384,385,389,390,391,395,396,397,401
%N A194384 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) > 0, where r=sqrt(8) and < > denotes fractional part.
%C A194384 See A194368.
%t A194384 r = Sqrt[8]; c = 1/2;
%t A194384 x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
%t A194384 y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
%t A194384 t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 100}];
%t A194384 Flatten[Position[t1, 1]]   (* A194381 *)
%t A194384 t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];
%t A194384 Flatten[Position[t2, 1]]   (* A194382 *)
%t A194384 %/2  (* A194383 *)
%t A194384 t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 600}];
%t A194384 Flatten[Position[t3, 1]]   (* A194384 *)
%Y A194384 Cf. A010466, A194368, A194381, A194382, A194383.
%K A194384 nonn
%O A194384 1,1
%A A194384 _Clark Kimberling_, Aug 23 2011