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A194421 Numbers m such that Sum_{k=1..m} (<1/3 + k*r> - <k*r>) > 0, where r=sqrt(5) and < > denotes fractional part. 4

%I

%S 1,2,7,10,11,13,14,15,16,17,18,19,20,22,23,24,25,26,27,28,29,30,31,32,

%T 33,34,35,36,37,38,39,40,41,43,44,45,46,47,48,49,50,51,52,53,54,55,56,

%U 57,58,61,62,64,65,66,67,68,69,70,71,73,74,79,82,83,85,86,87

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

%C See A194368.

%t r = Sqrt[5]; 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, 1000}];

%t Flatten[Position[t1, 1]] (* A194419 *)

%t t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 700}];

%t Flatten[Position[t2, 1]] (* A194420 *)

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

%t Flatten[Position[t3, 1]] (* A194421 *)

%Y Cf. A194368.

%K nonn

%O 1,2

%A _Clark Kimberling_, Aug 24 2011

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Last modified January 27 08:21 EST 2022. Contains 350606 sequences. (Running on oeis4.)