It is very surprising that distributions such as Fibonacci and the powers of two follow this law. Some number sequences that don't are numbers like pi and e. These numbers are said to be normal numbers, meaning they have an equal distribution amongst all digits. However, this hasn't been rigorously proven and is still an open problem.[1]
The distribution of the digits of pi and e is not the same as the distribution of first digits in a set of numbers; only the second is subject to Benford's Law. While both normal numbers and Benford's Law are interesting mathematical objects and deal with distributions of digits in a number, that is the complete extent to which they are related.
Just about any distribution where the distance between sequential numbers grows as the numbers grow will follow the law. Fibonacci and powers of two both fit that.
Comments
It is very surprising that distributions such as Fibonacci and the powers of two follow this law. Some number sequences that don't are numbers like pi and e. These numbers are said to be normal numbers, meaning they have an equal distribution amongst all digits. However, this hasn't been rigorously proven and is still an open problem.[1]
http://en.m.wikipedia.org/wiki/Normal_number
The distribution of the digits of pi and e is not the same as the distribution of first digits in a set of numbers; only the second is subject to Benford's Law. While both normal numbers and Benford's Law are interesting mathematical objects and deal with distributions of digits in a number, that is the complete extent to which they are related.
Just about any distribution where the distance between sequential numbers grows as the numbers grow will follow the law. Fibonacci and powers of two both fit that.