Stoneham number

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In mathematics, the Stoneham numbers are a certain class of real numbers, named after mathematician R. Stoneham. For coprime numbers b, c > 1, the Stoneham number αb,c is defined as

\alpha_{b,c} = \sum_{n=c^k>1} \frac{1}{b^nn} = \sum_{k=1}^\infty \frac{1}{b^{c^k}c^k}

It was shown by Stoneham in 1973 that αb,c is b-normal whenever c is an odd prime and b is a primitive root of c2.

[edit] References

  • R. Stoneham, On absolute (j,∈)-normality in the rational fractions with applications to normal numbers, Acta arithmetica, vol. 22 (1973), pp. 277-286
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