# Champernowne’s constant

For a given base $b$, Champernowne’s constant $C_{b}$ is the result of concatenating the base $b$ digits of the positive integers in order after 0 and a decimal point, that is,

 $\sum_{i=1}^{\infty}\frac{i}{b^{\sum_{j=1}^{i}k}}$

(where $k$ is the number of digits of $j$ in base $b$).

Kurt Mahler proved that $C_{10}$ (approximately 0.123456789101112131415161718192021…) is a transcendental number. Champernowne had earlier proved that $C_{10}$ is a normal number.

Title Champernowne’s constant ChampernownesConstant 2013-03-22 17:04:09 2013-03-22 17:04:09 PrimeFan (13766) PrimeFan (13766) 4 PrimeFan (13766) Definition msc 11A63 Champernowne constant