Llei de Benford

Abstract

This work is about Benford’s Law (also know as first digit law) that asserts that, in some situations, the fraction of numbers that start with the digit $d$ is not the intuitively –and yet reasonable– 1/9 but the remarkable log $_{10} (1 + d ^{−1} )$. We also study, in a generalized way, the behaviour of the others digits and we will see how certains sequences (Fibonacci’s numbers, powers, etc) follows almost perfectly the values predicted by the law. Finally we will discuss daily situations that also follows the Benford’s Law (lists populations, payments, etc).