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Strings of first digits of powers of a number. (English) Zbl 0547.10005
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.