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A194398 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) < 0, where r=sqrt(15) and < > denotes fractional part.

%I A194398 #10 Feb 15 2021 02:18:54
%S A194398 1,2,3,4,5,9,10,11,12,13,17,18,19,20,21,25,26,27,28,29,33,34,35,36,37,
%T A194398 41,42,43,44,45,49,50,51,52,53,57,58,59,60,61,63,64,65,66,67,68,69,71,
%U A194398 72,73,74,75,76,77,79,80,81,82,83,84,85,87,88,89,90,91,92,93
%N A194398 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) < 0, where r=sqrt(15) and < > denotes fractional part.
%C A194398 See A194368.
%t A194398 r = Sqrt[15]; c = 1/2;
%t A194398 x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
%t A194398 y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
%t A194398 t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 100}];
%t A194398 Flatten[Position[t1, 1]]       (* A194398 *)
%t A194398 t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 800}];
%t A194398 Flatten[Position[t2, 1]]       (* A194399 *)
%t A194398 t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 800}];
%t A194398 Flatten[Position[t3, 1]]       (* A194400 *)
%Y A194398 Cf. A010472, A194368, A194399, A194400.
%K A194398 nonn
%O A194398 1,2
%A A194398 _Clark Kimberling_, Aug 24 2011