Prime numbers along Rudin-Shapiro sequences (Q891765)

Summary: For a large class of digital functions \(f\), we estimate the sums \(\sum_{n \leq x} \Lambda(n) f(n)\) (and \(\sum_{n \leq x} \mu(n) f(n)\)), where \(\Lambda\) denotes the von Mangoldt function (and \(\mu\) the Möbius function). We deduce from these estimates a prime number theorem (and a Möbius randomness principle) for sequences of integers with digit properties including the Rudin-Shapiro sequence and some of its generalizations.