Does anyone know the size of this set or how to figure it out:
$$ \left\{0.a_1a_2a_3\dots \colon \sum_{i=2}^{\infty}\frac{1}{G_i}\in\mathbb{R}\right\},$$ where $G_i=(9-a_{(\sum_{j=1}^{i-1}j)+1})\dots(9-a_{(\sum_{j=1}^{i-1}j)+i})$ and if $G_i=0$, define $\frac{1}{G_i} = 0$.
e.g. for $ 0.\dot{1}21314151617181\dot{9}\dots$, $G_2=(9-2)(9-1)=78$, $G_3=(9-3)(9-1)(9-4)=685$, $G_4=(9-1)(9-5)(9-1)(9-6)=8483$ and so on.