Nice article, even though I'm coming across it 20 years after it was written. Here's another way to get a distribution that favors numbers starting with 1, then 2, etc.

Generate sets of random numbers according to the following scheme.
1. Select a range, 0 to n for some n.
2. Select k numbers in that range at random.
3. Repeat indefinitely.

How do you select n, the top of the range? Make that random in the range, say, 0 .. 99.
Any n will allow selection only of numbers from 0 .. n. So higher number, i.e., those greater than n will be excluded.

Given that we are performing this process multiple times, with a new n each time, when we aggregate all the random number collections it will include all numbers. But lower numbers will be more frequent than higher numbers because we select the top of the range to exclude larger numbers.

I haven't tried this experimentally. I wonder how close it would come to Benford's Law.

Nice article, even though I'm coming across it 20 years after it was written. Here's another way to get a distribution that favors numbers starting with 1, then 2, etc.

Generate sets of random numbers according to the following scheme.

1. Select a range, 0 to n for some n.

2. Select k numbers in that range at random.

3. Repeat indefinitely.

How do you select n, the top of the range? Make that random in the range, say, 0 .. 99.

Any n will allow selection only of numbers from 0 .. n. So higher number, i.e., those greater than n will be excluded.

Given that we are performing this process multiple times, with a new n each time, when we aggregate all the random number collections it will include all numbers. But lower numbers will be more frequent than higher numbers because we select the top of the range to exclude larger numbers.

I haven't tried this experimentally. I wonder how close it would come to Benford's Law.