A194466 - OEIS

%I #9 Feb 14 2021 20:51:33

%S 3,5,6,10,17,20,22,23,27,29,30,32,33,34,35,36,37,39,40,44,46,47,51,58,

%T 61,63,64,68,75,92,99,102,104,105,109,116,119,121,122,126,128,129,131,

%U 132,133,134,135,136,138,139,143,145,146,150,157,160,162,163

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

%C See A194368.

%t r = Sqrt[2]; 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]]    (* A184465 *)

%t t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 200}];

%t Flatten[Position[t3, 1]]    (* A184466 *)

%Y Cf. A194368.

%K nonn

%O 1,1

%A _Clark Kimberling_, Aug 24 2011