Common
Champernowne constant
Transcendental number(s) with all positive integers in order
Champernowne constant
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. The number is defined by concatenating the base-10 representations of the positive integers: C10 = 0.1234567891011121314151617181920... (sequence A033307 in the OEIS). Champernowne constants can also be constructed in other bases similarly; for example, C2 = 0.11011100101110111... 2 and 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...
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