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A194373 Numbers n such that Sum_{k=1..n} (<1/2 + k*r> - <k*r>) > 0, where r=sqrt(3) and < > denotes fractional part. 4

%I

%S 3,7,11,29,33,37,41,43,44,45,47,48,49,51,52,53,55,59,63,67,85,89,93,

%T 97,99,100,101,103,104,105,107,108,109,111,115,119,123,141,145,149,

%U 153,155,156,157,159,160,161,163,164,165,167,171,175,179,197

%N Numbers n such that Sum_{k=1..n} (<1/2 + k*r> - <k*r>) > 0, where r=sqrt(3) and < > denotes fractional part.

%C See A194368.

%H G. C. Greubel, <a href="/A194373/b194373.txt">Table of n, a(n) for n = 1..1000</a>

%t r = Sqrt[3]; 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]] (* A194371 *)

%t t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 800}];

%t Flatten[Position[t2, 1]] (* A194372 *)

%t t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}];

%t Flatten[Position[t3, 1]] (* A194373 *)

%o (PARI) isok(n) = sum(k=1, n, frac(1/2+k*sqrt(3)) - frac(k*sqrt(3))) > 0; \\ _Michel Marcus_, Sep 10 2018

%Y Cf. A194368, A194371.

%K nonn

%O 1,1

%A _Clark Kimberling_, Aug 23 2011

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Last modified June 5 03:12 EDT 2020. Contains 334828 sequences. (Running on oeis4.)