Are the Digits of π an Independent and Identically Distributed Sequence?
Ted Jaditz · The American Statistician · 2000
This article searches for dependence in the decimal expansion of the number π. We systematically test whether the digits of π are k-distributed for greater and greater k. As it happens, testing whether longer and longer sequences are randomly distributed is a surprisingly interesting problem. We look at a number of approaches to testing independence and find no significant departures from uniform iid behavior in sequences up to 16 digits in length.