A Liouville number is a number which can be approximated very closely be a sequence of rational numbers (here is the rigorous definition I am working off of: http://en.wikipedia.org/wiki/Liouville_number).
I'm looking for an example of a Liouville number which cannot be approximated by a sequence of rational numbers with a denominators which are all a constant c multiplied by powers of some number a.
For instance, the Louiville constant ($0.110001000000000000000001$...) can be approximated by the sequence $\frac{1}{10}$, $\frac{11}{10^2}$, $\frac{110001}{10^6}$, etc, which is not what I am looking for because in each case the denominator is a power of $10$. In this case, we would say that $c=1$, $a=10$, and the denominator is always of the form $c \cdot a^n$ for some positive $n$.