cp's OEIS Frontend

A194758 Number of k such that {k*log(2)} < {n*log(2)}, where { } = fractional part.

%I A194758 #5 Mar 30 2012 18:57:44
%S A194758 1,1,1,4,3,2,7,5,3,10,7,4,1,11,7,3,15,10,5,19,13,7,23,16,9,2,21,13,5,
%T A194758 26,17,8,31,21,11,36,25,14,3,31,19,7,37,24,11,43,29,15,49,34,19,4,41,
%U A194758 25,9,48,31,14,55,37,19,62,43,24,5,51,31,11,59,38,17,67,45,23,75
%N A194758 Number of k such that {k*log(2)} < {n*log(2)}, where { } = fractional part.
%t A194758 r = Log[2]; p[x_] := FractionalPart[x];
%t A194758 u[n_, k_] := If[p[k*r] <= p[n*r], 1, 0]
%t A194758 v[n_, k_] := If[p[k*r] > p[n*r], 1, 0]
%t A194758 s[n_] := Sum[u[n, k], {k, 1, n}]
%t A194758 t[n_] := Sum[v[n, k], {k, 1, n}]
%t A194758 Table[s[n], {n, 1, 100}]   (* A194758 *)
%t A194758 Table[t[n], {n, 1, 100}]   (* A194759 *)
%Y A194758 Cf. A194759, A194738.
%K A194758 nonn
%O A194758 1,4
%A A194758 _Clark Kimberling_, Sep 02 2011