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