A194408 - OEIS

%I #8 Feb 15 2021 21:23:09

%S 7,13,14,15,19,20,21,22,23,25,26,27,28,29,30,31,32,33,34,35,36,37,38,

%T 39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,

%U 62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82

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

%C See A194368.

%t r = Pi; 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]]         (* A194408 *)

%t t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 1500}];

%t Flatten[Position[t2, 1]]         (* A194409 *)

%t t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 1500}];

%t Flatten[Position[t3, 1]]         (* A194410 *)

%Y Cf. A194368.

%K nonn

%O 1,1

%A _Clark Kimberling_, Aug 24 2011