A Note on Benford’s Law for Second Order Linear Recurrences with Perodical Coefficients

where and (b a ) are given real sequences with a common period r, = a n and bn , r = b. Linear recurrences of such type arise,e.g.,in the theory of continued fractions.lfw Is quadratic irrational,then the numerators and the denominators of the n-th convergent p/q of the continued fraction of u fulfil the relation (1) with b = I and a periodic positive integer sequence (a n ) (cf.,e.g.,[4Satz I/p.S and Satz 28 /p.52]).Llnear recurrences with periodical coefficients are also treated in [lip.148-ISO]. The sequence (u n ) is said to obey Benford's law i f