cp's OEIS Frontend

A194407 Numbers m such that Sum_{k=1..m} (<1/2 + k*e> - ) > 0 where < > denotes fractional part.

%I A194407 #9 Feb 15 2021 21:23:20
%S A194407 3,7,9,10,11,13,14,15,16,17,18,19,20,21,22,23,24,25,27,28,29,31,35,39,
%T A194407 41,42,43,45,46,47,48,49,50,51,52,53,54,55,56,57,59,60,61,63,67,81,85,
%U A194407 87,88,89,91,92,93,95,99,113,117,119,120,121,123,124,125,127
%N A194407 Numbers m such that Sum_{k=1..m} (<1/2 + k*e> - <k*e>) > 0 where < > denotes fractional part.
%C A194407 See A194368.
%t A194407 r = E; c = 1/2;
%t A194407 x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
%t A194407 y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
%t A194407 t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 200}];
%t A194407 Flatten[Position[t1, 1]]       (* A194405 *)
%t A194407 t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 200}];
%t A194407 Flatten[Position[t2, 1]]       (* A194406 *)
%t A194407 t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 200}];
%t A194407 Flatten[Position[t3, 1]]       (* A194407 *)
%Y A194407 Cf. A194368.
%K A194407 nonn
%O A194407 1,1
%A A194407 _Clark Kimberling_, Aug 24 2011