Prime numbers along Rudin–Shapiro sequences

International audienceFor a large class of digital functions f, we estimate the sums Sigma(n <= x) Lambda(n)f (n) (and Sigma(n <= x) mu(n)f (n)), where Lambda denotes the von Mangoldt function (and mu, the Mobius function). We deduce from these estimates a Prime Number Theorem (and a Mobius randomness principle) for sequences of integers with digit properties including the Rudin-Shapiro sequence and some of its generalizations