The first digit problem for prime numbers. (Le problème du premier chiffre décimal pour les nombres premiers.) (French) Zbl 0838.11004
For a class of sequences, defined as unions of intervals \([p_n, q_n]\) with the assumptions \(q_{n - 1}/q_n \to \rho\), \(p_n/q_n \to \sigma\), \(0 <\rho < \sigma < 1\), the lower and upper asymptotic densities and the logarithmic density are calculated. It is shown that the primes in such a set have the same relative densities within the set of primes.
Reviewer: I.Z.Ruzsa (Budapest)
MSC:
11B05 | Density, gaps, topology |
11K16 | Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. |