Champernowne's constant

In mathematics, the Champernowne constant C₁₀ is a transcendental real constant whose decimal expansion has important properties. It is named after economist and mathematician D. G. Champernowne, who published it as an undergraduate in 1933.

For base 10, the number is defined by concatenating representations of successive integers:

Champernowne constants can also be constructed in other bases, similarly, for example:

The Champernowne constants can be expressed exactly as infinite series:

where ${\displaystyle \lceil {x}\rceil =}$ ceiling(${\displaystyle x}$), ${\displaystyle 10_{b}^{~x}=b^{x}}$ in base 10, ${\displaystyle \log _{10_{b}}(x)=\log _{b_{10}}(x)}$ and ${\displaystyle b}$ is the base of the constant.

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