Strings of first digits of powers of a number (Q798691)

Let a and r be positive integers. Consider the sequence \(\{f_ n\}\) of first digits obtained by taking the infinite sequence \(\{a^ n\}\) to base r. Properties of \(\{f_ n\}\) are investigated - such as the ''probability'' of occurrence of a specified finite sequence of digits among the \(\{f_ n\}\). A state transition graph can be associated with each sequence \(\{f_ n\}\). Properties of these graphs are utilized by the author to calculate these probabilities.