The first few terms in the continued fraction of the Champernowne constant are [0; 8, 9, 1, 149083, 1, 1, 1, 4, 1, 1, 1, 3, 4, 1, 1, 1, 15, 45754...10987, 6, 1, 1, 21, ...] (OEIS A030167), and the number of decimal digits in these terms are 0, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 166, 1, ... (OEIS A143532). E. W. Weisstein computed terms of the continued fraction on Jun. 30, 2013 using the Wolfram Language.
First occurrences of the terms 1, 2, 3, ... in the continued fraction occur at , 28, 13, 9, 93, 20, 31, 2, 3, 339, 71, 126, 107, ... (OEIS A038706). The smallest unknown value is 188, which has .
The continued fraction contains sporadic very large terms, making the continued fraction difficult to calculate. However, the size of the continued fraction highwater marks display apparent patterns (Sikora 2012). Large terms greater than occur at positions 5, 19, 41, 102, 163, 247, 358, 460, ... and have 6, 166, 2504, 140, 33102, 109, 2468, 136, ... digits, respectively.
The highwater marks in terms of the continued fraction occur for terms 0, 1, 2, 4, 18, 40, 162, 526, 1708, 4838, 13522, 34062, ... (OEIS A143533; Sikora 2012), which have 0, 1, 1, 6, 166, 2504, 33102, 411100, 4911098, 57111096, 651111094, 7311111092, ... (OEIS A143534; Sikora 2012) decimal digits, respectively. Sikora (2012) conjectured that the number of decimal digits in the th highwater mark for are given by
(1)

where
(2)
 
(3)

in agreement with known calculated values up to .