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.
Reviewer: K.Alladi


11A63 Radix representation; digital problems
11K16 Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc.
05C75 Structural characterization of families of graphs
05C20 Directed graphs (digraphs), tournaments