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Fractal change-of-base functions. (English) Zbl 1318.11007

Summary: This note introduces possibly new “change of base functions” that have self-similar graphs. If the two bases are positive integers, then such functions map rational numbers to rational numbers in interesting ways, with connections to Cantor sets. Three open number-theoretic questions are stated.

MSC:

11A63 Radix representation; digital problems
11A41 Primes
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