Definition:Champernowne Constant

From ProofWiki
Jump to navigation Jump to search

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