## The Annals of Probability

### The Distribution of Leading Digits and Uniform Distribution Mod 1

Persi Diaconis

#### Abstract

The lead digit behavior of a large class of arithmetic sequences is determined by using results from the theory of uniform distribution $\operatorname{mod} 1$. Theory for triangular arrays is developed and applied to binomial coefficients. A conjecture of Benford's that the distribution of digits in all places tends to be nearly uniform is verified.

#### Article information

Source
Ann. Probab., Volume 5, Number 1 (1977), 72-81.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176995891

Digital Object Identifier
doi:10.1214/aop/1176995891

Mathematical Reviews number (MathSciNet)
MR422186

Zentralblatt MATH identifier
0364.10025

JSTOR