Journal of Integer Sequences, Vol. 16 (2013), Article 13.2.15

The Many Faces of the Kempner Number

Boris Adamczewski
CNRS, Université de Lyon, Université Lyon 1
Institut Camille Jordan
43 boulevard du 11 novembre 1918
69622 Villeurbanne Cedex


In this survey, we present five different proofs for the transcendence of Kempner's number, defined by the infinite series Σn ≥ 0 1/22n. 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.

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(Concerned with sequences A000079 A006466 A007400 A007404 A076214.)

Received September 30 2012; revised version received January 13 2013. Published in Journal of Integer Sequences, March 2 2013.

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