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

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 $$n$$ .