123456789

In mathematics, the Champernowne constant C10 is a transcendental real constant whose decimal expansion has important properties. It is named after economist and mathematician D. G. Champernowne, who published it as an undergraduate in 1933.For base 10, the number is defined by concatenating representations of successive integers:

C10 = 0.12345678910111213141516…  (sequence A033307 in the OEIS).Champernowne constants can also be constructed in other bases, similarly, for example:

C2 = 0.11011100101110111… 2
C3 = 0.12101112202122… 3.The Champernowne word or Barbier word is the sequence of digits of C10, obtained by writing it in base 10 and juxtaposing the digits:
12345678910111213141516...  (sequence A007376 in the OEIS)More generally, a Champernowne sequence (sometimes also called a Champernowne word) is any sequence of digits obtained by concatenating all finite digit-strings (in any given base) in some recursive order.
For instance, the binary Champernowne sequence in shortlex order is

0 1 00 01 10 11 000 001 ... (sequence A076478 in the OEIS)where spaces (otherwise to be ignored) have been inserted just to show the strings being concatenated.

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