Parry Expansions of Polynomial Sequences

We prove that the sum-of-digits function with respect to certain digital expansions (which are related to linear recurrences) and similarly defined functions evaluated on polynomial sequences of positive integers or primes satisfy a central limit theorem. These digital expansions are special cases of numeration systems associated to primitive substitutions on finite alphabets, the digits of which form Markov chains and induce Markov partitions of the torus T^d. We provide an algorithm to determine the (fractal) boundary of these partitions.