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A note on Benford’s law for second order linear recurrences with periodical coefficients. (English) Zbl 0754.11021
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.
Reviewer: R.F.Tichy (Graz)

##### MSC:
 11K06 General theory of distribution modulo $$1$$ 11B37 Recurrences
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