A note on Benford's law for second order linear recurrences with periodical coefficients (Q1188392)

A sequence \((u_ n)^ \infty_{n=1}\) satisfies Benford's law if \((\log_{10}| u_ n|)\) is uniformly distributed modulo 1. For second-order linear recurrences \(u_{n+2}=a_{n+2}u_{n+1}+b_{n+2}u_ n\) with periodic coefficients \(a_{n+2}, b_{n+2}\) the authors prove a sufficient criterion for \((u_ n)\) satisfying Benford's law. As a corollary the sequences \((p_ n)\) and \((q_ n)\), where \(p_ n/q_ n\) denotes the \(n\)-th convergent of the continued fraction expansion of a quadratic irrational, satisfy Benford's law.