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A194418 Numbers m such that Sum_{k=1..m} (<1/3 + k*r> - <k*r>) > 0, where r=sqrt(3) and < > denotes fractional part. 5

%I

%S 7,10,11,13,14,22,25,26,28,29,37,40,41,43,44,52,55,67,70,82,85,97,100,

%T 160,163,164,166,167,175,178,179,181,182,190,193,194,196,197,205,208,

%U 220,223,235,238,250,253,373,376,388,391,403,406

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

%C See A194368.

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

%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, 150}];

%t Flatten[Position[t1, 1]] (* A194415 *)

%t t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];

%t Flatten[Position[t2, 1]] (* A194416 *)

%t %/3 (* A194417 *)

%t t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 500}];

%t Flatten[Position[t3, 1]] (* A194418 *)

%Y Cf. A194368.

%K nonn

%O 1,1

%A _Clark Kimberling_, Aug 24 2011

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Last modified May 20 01:04 EDT 2022. Contains 353847 sequences. (Running on oeis4.)