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A194398 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) < 0, where r=sqrt(15) and < > denotes fractional part. 4

%I

%S 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 41,42,43,44,45,49,50,51,52,53,57,58,59,60,61,63,64,65,66,67,68,69,71,

%U 72,73,74,75,76,77,79,80,81,82,83,84,85,87,88,89,90,91,92,93

%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, A194399, A194400.

%K nonn

%O 1,2

%A _Clark Kimberling_, Aug 24 2011

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Last modified September 22 17:26 EDT 2021. Contains 347607 sequences. (Running on oeis4.)