Distributions That Exactly Satisfy Benford's Law
Some well-known infinite integer sequences provably satisfy Benford's law exactly (in the asymptotic limit as more and more terms of the sequence are included). Among these are the Fibonacci numbers, the factorials, the powers of 2, and the powers of almost any other number.
Likewise, some continuous processes satisfy Benford's law exactly (in the asymptotic limit as the process continues longer and longer). One is an exponential growth or decay process: If a quantity is exponentially increasing or decreasing in time, then the percentage of time that it has each first digit satisfies Benford's law asymptotically (i.e., more and more accurately as the process continues for more and more time).
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