The Ramanujan Journal

, Volume 37, Issue 1, pp 109–111 | Cite as

Addendum to: On the rational approximation of the sum of the reciprocals of the Fermat numbers

Article

Abstract

As a corollary of the main result of our recent paper, On the rational approximation of the sum of the reciprocals of the Fermat numbers published in this same journal, we prove that for each integer \(b\ge 2\) the irrationality exponent of \(\sum _{n\geqslant 0} s_2(n)/b^n\) is equal to 2, where \(s_2(n)\) is the sum of the binary digits on \(n\).

Keywords

Irrationality exponents Fermat numbers Binary expansions 

Mathematics Subject Classification

11J82 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.School of Mathematical and Physical SciencesUniversity of NewcastleCallaghanAustralia

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