# Definition:Champernowne Constant

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## Definition

The **Champernowne constant** is the real number whose decimal expansion is formed by concatenating the positive integers in asccending order:

- $C_{10} = 0 \cdotp 12345 \, 67891 \, 01112 \, 13141 \, 51617 \, 18192 \, 02122 \ldots$

This sequence is A033307 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

## Also known as

The **Champernowne constant** is also known as **Mahler's number** for Kurt Mahler, who proved it transcendental in $1937$.

## Also see

## Source of Name

This entry was named for David Gawen Champernowne.

## Sources

- 1933: D.G. Champernowne:
*The Construction of Decimals Normal in the Scale of Ten*(*J. London Math. Soc.***Vol. 8**: 254 – 260) - 1983: François Le Lionnais and Jean Brette:
*Les Nombres Remarquables*... (previous) ... (next): $0,1234567891011 \ldots$