Linear recurrence relations, primitivity and Benford's law

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.