Sum of reciprocals of continued fraction of harmonic numbers

[Leroy Quet]

Let a(n) be the sum of reciprocals of the terms of the continued fraction
of H(n) = sum{k=1 to n} 1/k.
(I just submitted the first couple terms of the
numerator and denominator sequences to the Encyclopedia of
Integer Sequences.)


So, for example, 1 +1/2 +1/3 +1/4 +1/5 +1/6 = 49/20 =
2 + 1/(2 + 1/(4 + 1/2)).
So a(6) = 7/4 = 1/2 + 1/2 + 1/4 + 1/2.

What I am wondering is if there is a maximum and/or minimum term
of {a(k)}.

I am also just curious when the first term = to 1 is, if any terms equals 
1.

thanks,
Leroy Quet