A194370 - OEIS

%I #9 Feb 15 2021 20:03:19

%S 1,3,5,6,7,8,9,10,11,13,15,17,18,19,20,21,22,23,25,27,29,30,31,32,33,

%T 34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,

%U 57,58,59,60,61,62,63,64,65,66,67,68,69,71,73,75,76,77,78,79,80

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

%C See A194368.

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

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

%t Flatten[Position[t2, 1]] (* A194368 *)

%t %/2 (* A194369 *)

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

%t Flatten[Position[t3, 1]] (* A194370 *)

%Y Cf. A194368.

%K nonn

%O 1,2

%A _Clark Kimberling_, Aug 23 2011