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A194375 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) > 0, where r=sqrt(5) and < > denotes fractional part.

%I A194375 #10 Feb 15 2021 02:20:06
%S A194375 1,2,3,5,6,7,9,10,11,13,14,15,17,18,19,20,21,22,23,24,25,26,27,28,29,
%T A194375 30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,
%U A194375 53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,73,74
%N A194375 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) > 0, where r=sqrt(5) and < > denotes fractional part.
%C A194375 See A194368.
%t A194375 r = Sqrt[5]; c = 1/2;
%t A194375 x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
%t A194375 y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
%t A194375 t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 500}];
%t A194375 Flatten[Position[t1, 1]]   (* empty *)
%t A194375 t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 400}];
%t A194375 Flatten[Position[t2, 1]]   (* A194374 *)
%t A194375 t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}];
%t A194375 Flatten[Position[t3, 1]]   (* A194375 *)
%Y A194375 Cf. A194368, A194375.
%K A194375 nonn
%O A194375 1,2
%A A194375 _Clark Kimberling_, Aug 23 2011