Sur les occurrences des mots dans les nombres premiers
We generalize Mauduit and Rivat’s theorem on the Rudin–Shapiro sequence. Weakening the hypothesis needed in their theorem, we prove a prime number theorem for a large class of functions defined on the digits. Our result covers the case of generalized Rudin–Shapiro sequences as well as block-additive sequences on finite and infinite expansions. We also give a partial answer to a question posed by Kalai.