Benford's law for the $3x+1$ function

Abstract

We show that for most choices of an initial seed $x_0$, the sequence of the first $N$ iterates of $x_0$ under the $3x+1$ map approximately satisfies Benford's law.

16 pages; revised proof of Prop. 3.3

References in corpus (1)

• Benford's Law, Values of L-functions and the 3x+1 Problem

Cited by in corpus (2)

• The Modulo 1 Central Limit Theorem and Benford's Law for Products
• Benford's law from 1881 to 2006