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A194386 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) > 0, where r=sqrt(10) and < > denotes fractional part.

%I A194386 #10 Feb 15 2021 02:20:48
%S A194386 1,2,3,4,5,7,8,9,10,11,13,14,15,16,17,19,20,21,22,23,25,26,27,28,29,
%T A194386 31,32,33,34,35,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,
%U A194386 55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75
%N A194386 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) > 0, where r=sqrt(10) and < > denotes fractional part.
%C A194386 See A194368.
%t A194386 r = Sqrt[10]; c = 1/2;
%t A194386 x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
%t A194386 y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
%t A194386 t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 300}];
%t A194386 Flatten[Position[t1, 1]]   (* empty *)
%t A194386 t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 400}];
%t A194386 Flatten[Position[t2, 1]]     (* A194385 *)
%t A194386 t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}];
%t A194386 Flatten[Position[t3, 1]]     (* A194386 *)
%Y A194386 Cf. A010467, A194368, A194385.
%K A194386 nonn
%O A194386 1,2
%A A194386 _Clark Kimberling_, Aug 23 2011