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A194468 Numbers m such that Sum_{k=1..m} (<c + k*r> - <k*r>) > 0, where r=sqrt(3) and c=sqrt(1/3), and < > denotes fractional part. 1

%I

%S 7,11,14,26,52,97,104,108,111,123,149,153,156,160,163,164,165,167,175,

%T 179,182,194,201,205,208,220,317,362,369,373,376,388,414,582,679,724,

%U 731,735,738,750,776

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

%C See A194368.

%t Remove["Global`*"];

%t r = Sqrt[3]; c = 1/r;

%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, 200}];

%t Flatten[Position[t1, 1]] (* A184467 *)

%t t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 900}];

%t Flatten[Position[t3, 1]] (* A184468 *)

%Y Cf. A194368.

%K nonn

%O 1,1

%A _Clark Kimberling_, Aug 24 2011

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Last modified October 21 15:46 EDT 2021. Contains 348155 sequences. (Running on oeis4.)