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

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

2005-09-07

arxiv.org/abs/math/0509175v2

J. London Math. Soc. 74 (2006), 289--303

Mathematics

Number Theory

16 pages; revised proof of Prop. 3.3

Scientific paper

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.

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