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

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

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 "c"².

References

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