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# 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.

Synonym:

Champernowne constant

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

11A63*no label found*

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