Relations de récurrence linéaires, primitivité et loi de Benford

Abstract

We prove that many sequences of positive numbers $(a_n)$ defined by finite linear difference equations $a_{n+k}=c_{k-1}{a}_{n+k-1}+...+c_0{a}_n$ with suitable non negative reals coefficients $c_i$ satisfy Bendford's Law on the first digit in many bases $b>2$. Our techniques rely on Perron-Frobenius theory via the companion matrix of the characteristic polynomial of the defining equation.

12 pages; title updated, theorem 2 completed