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

Jeffrey C. Lagarias·K. Soundararajan
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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.

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Jeffrey C. Lagarias, K. Soundararajan. 2006-08-09. Benford's law for the $3x+1$ function. https://arxiv.org/abs/math/0509175

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