The formula for 1 + a + a^2 + .... where 0 < a < 1 is $\frac{1}{1-a}$, but what if you wanted to sum only those where the exponent is a power of 2? That is,

$S = a + a^2 + a^4 + a^8 + \cdots$

I feel like this is an easy one but I just can't seem to find a closed expression for it, nor search for it on Google.