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A194400 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) > 0, where r=sqrt(15) and < > denotes fractional part.

%I A194400 #10 Feb 15 2021 02:19:09
%S A194400 7,15,23,31,39,47,55,377,385,393,401,409,417,425,433,439,440,441,447,
%T A194400 448,449,455,456,457,463,464,465,471,472,473,479,480,481,487,488,489,
%U A194400 495,503,511,519,527,535,543,551
%N A194400 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) > 0, where r=sqrt(15) and < > denotes fractional part.
%C A194400 See A194368.
%t A194400 r = Sqrt[15]; c = 1/2;
%t A194400 x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
%t A194400 y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
%t A194400 t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 100}];
%t A194400 Flatten[Position[t1, 1]]       (* A194398 *)
%t A194400 t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 800}];
%t A194400 Flatten[Position[t2, 1]]       (* A194399 *)
%t A194400 t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 800}];
%t A194400 Flatten[Position[t3, 1]]       (* A194400 *)
%Y A194400 Cf. A010472, A194368, A194398, A194399.
%K A194400 nonn
%O A194400 1,1
%A A194400 _Clark Kimberling_, Aug 24 2011