Definition:Champernowne Constant

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The Champernowne constant is the real number whose decimal expansion is formed by concatenating the positive integers in ascending 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 $1937$.

Some sources report it as Champernowne's number.

Also see

  • Results about the Champernowne constant can be found here.

Source of Name

This entry was named for David Gawen Champernowne.

Historical Note

The Champernowne constant was invented by David Gawen Champernowne as an example of a real number which can be demonstrated to be normal with respect to base $10$.

He achieved this in $1933$ while still an undergraduate.