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Sur le problème du premier chiffre décimal. (French) Zbl 0557.60011
Given \(E_k\), the set of positive integers whose first digit is \(k\), its asymptotic density does not exist (as it is well-known). In this paper it is proved that the analytical density \(d(E_ k)\) exists, with \(d(E_k)=\log_{10}(1+1/k)\), in accordance with known empirical results (the so-called ”first-digit problem”).
Reviewer: R.Scozzafava

MSC:
60B99 Probability theory on algebraic and topological structures
11K16 Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc.
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