The decimal digits of the Champernowne constant 
begin
 |
(OEIS A033307).
The Earls sequence (starting position of 
consecutive copies of the decimal
representation of the positive integer 
) for 
is given for 
, 2, ... by 1, 34, 56, 1222, 1555, 25554, 29998, 433330,
7988888882, 1101010101010, ... (OEIS A224896).
The starting positions of the first occurrence of the decimal representation of 
, 1, 2, ... in the decimal
expansion of 
(not including the initial 0 to the left of the decimal
point) are 11, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 1, ... (OEIS A229186).
Scanning the fractional decimal expansion of 
until all strings of 
decimal digits, including
those with leading zeros, have occurred, the last strings
of 1, 2, ... decimal digits appearing are 0, 00,
000, 0000, ..., which end at decimal digits 11,
192, 2893, 38894, 488895, ... (OEIS A072290).
The first few starting positions of the sequence of decimal digits 0123456789 are 11234567799, 22345677908, 33456779017, 44567790126, 55677901235, 66779012344, ... and those of 9876543210 are 7777777779, 9876543212, 19987654323, 30998765434, 42099876545, 53209987656, 64320998767, ... (E. Weisstein, Jul. 26, 2013).
Reported 
-constant primes or probable
primes have 10, 14, 24, 235, 2804, 4347, 37735, ... (OEIS A071620)
decimal digits.
It is known that the Champernowne constant is normal in base 10 (Champernowne 1933, Bailey
and Crandall 2002), though the following table giving the counts of decimal
digits in the first 
fractional decimal digits
shows unequal finite frequencies through 
decimal digits, with an
excess of 1s and a deficit of 0s when cutting the decimal-digit string off at locations such as 
.
 | OEIS | 10 | 100 |  |  |  |  |  |  |  |
| 0 | 0 | 5 | 66 | 747 | 8642 | 83528 | 884151 | 9234568 | 96021948 | |
| 1 | 2 | 16 | 177 | 1858 | 19753 | 179810 | 1582562 | 14234568 | 130589850 | |
| 2 | 1 | 16 | 177 | 1636 | 11111 | 94539 | 995260 | 10345679 | 100589849 | |
| 3 | 1 | 16 | 148 | 858 | 8642 | 94539 | 995161 | 10234568 | 96589849 | |
| 4 | 1 | 16 | 77 | 858 | 8642 | 94539 | 995160 | 9345679 | 96089849 | |
| 5 | 1 | 11 | 77 | 858 | 8642 | 93723 | 982462 | 9345679 | 96029849 | |
| 6 | 1 | 5 | 77 | 858 | 8642 | 93538 | 895160 | 9345679 | 96022849 | |
| 7 | 1 | 5 | 67 | 833 | 8642 | 93538 | 894462 | 9345679 | 96022049 | |
| 8 | 1 | 5 | 67 | 747 | 8642 | 88718 | 891462 | 9333333 | 96021959 | |
| 9 | 1 | 5 | 67 | 747 | 8642 | 83528 | 884160 | 9234568 | 96021949 |
