Kimberling, Clark Fractal change-of-base functions. (English) Zbl 1318.11007 Adv. Appl. Math. Sci. 12, No. 5, 255-261 (2013). 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 Keywords:fractal; Cantor set; prime; change-of-base PDFBibTeX XMLCite \textit{C. Kimberling}, Adv. Appl. Math. Sci. 12, No. 5, 255--261 (2013; Zbl 1318.11007) Online Encyclopedia of Integer Sequences: Decimal representation of Sum{d(i)*3^i: i=0,1,...}, where Sum{d(i)*2^i: i=0,1,...} is the base 2 representation of sqrt(2).