A194758 - OEIS

%I #5 Mar 30 2012 18:57:44

%S 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 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 25,9,48,31,14,55,37,19,62,43,24,5,51,31,11,59,38,17,67,45,23,75

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

%t r = Log[2]; p[x_] := FractionalPart[x];

%t u[n_, k_] := If[p[k*r] <= p[n*r], 1, 0]

%t v[n_, k_] := If[p[k*r] > p[n*r], 1, 0]

%t s[n_] := Sum[u[n, k], {k, 1, n}]

%t t[n_] := Sum[v[n, k], {k, 1, n}]

%t Table[s[n], {n, 1, 100}]   (* A194758 *)

%t Table[t[n], {n, 1, 100}]   (* A194759 *)

%Y Cf. A194759, A194738.

%K nonn

%O 1,4

%A _Clark Kimberling_, Sep 02 2011