Stoneham number

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

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

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.

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