Sequence Involving Continued Fraction Recursion

[Leroy Quet]

Consider the following recursion.

Let r_1 = 1;

r_{n+1} = [r_1; r_2, r_3,..., r_n], 

a continued fraction, where the sequence {r_k} is a sequence of rationals.

The denominators of {r_k} is sequence A064846 of the On-Line Encyclopedia 
of Integer Sequences.

Let the m_th denominator be a(m).

Does d(m) always divide d(m+1) ?

Thanks,
Leroy Quet