New structural properties of strings generated by leading digits of 2N

摘要

Several new properties of the first decimal digits of the powers of 2 are presented. It is shown that the consecutive members of the sequence of the first digits of powers of 2 appear in one of five strings. Some statistical properties such as probabilities of occurrence of the strings, their transition probabilities, etc. are presented. The associated state transition graphs are also displayed. It is found that the process of generating strings follows a non-Markovian process but is ergodic. The relation of these properties to ergotic theory is mentioned, and possible applications to information theory, computer science, and statistical mechanics are briefly stated.