Stoneham number

In mathematics, the Stoneham numbers are a certain class of real numbers, named after mathematician Richard G. Stoneham (1920–1996).^[1] For coprime numbers b, c > 1, the Stoneham number α_b,c is defined as

${\displaystyle \alpha _{b,c}=\sum _{n=c^{k}>1}{\frac {1}{b^{n}n}}=\sum _{k=1}^{\infty }{\frac {1}{b^{c^{k}}c^{k}}}}$

It was shown by Stoneham in 1973 that α_b,c is b-normal whenever c is an odd prime and b is a primitive root of c². In 2002, Bailey & Crandall showed that coprimality of b, c > 1 is sufficient for b-normality of α_b,c.^[2]