A problem I've been working on has lead me to consider power series of the form $\sum_{n \geq 0} a_n x^n$ with $a_n = 0$ or $a_n = 1$ for all $n$.
Is there any literature available on these series? What do we know about them? I'm interested in convergence, analytic properties, and possibly even representation by known functions. Any help would be greatly appreciated.