The many faces of the Kempner number
arXiv:1303.1685
Abstract
In this survey, we present five different proofs for the transcendence of Kempner's number, defined by the infinite series $\sum_{n=0}^{\infty} \frac{1}{2^{2^n}}$. We take the opportunity to mention some interesting ideas and methods that are used for proving deeper results. We outline proofs for some of these results and also point out references where the reader can find all the details.
Published in a special issue of the Journal of Integer Sequences in honor of the 60th birthday of Jean-Paul Allouche