Copeland-Erdős Constant Digits
The Copeland-Erdős constant has decimal expansion
(OEIS A033308).
The Earls sequence (starting position of 
copies of the digit 
) for 
is given for 
, 2, ... by 5, 113, 1181, 21670, 263423, 7815547, 35619942, ... (OEIS A224897).
The digit sequences 0123456789 and 9876543210 do not occur in the first 
digits (E. Weisstein, Jul. 24, 2013).
-constant primes occur at 1, 2, 4, 11, 353, 355, 499, 1171, 1543, 5719, 11048, 68433, 97855, 292447, ... (OEIS A227530) decimal digits. There are no others with fewer than 
decimal digits (Rodenkirch, Jun. 18, 2016).
The starting positions of the first occurrence of 
, 1, 2, ... in the decimal expansion of 
(not counting the initial 0 to the left of the decimal point) are 48, 5, 1, 2, 21, 3, 31, 4, 41, 12, ... (OEIS A229190).
Scanning the decimal expansion of 
until all 
-digit numbers have occurred, the last 1-, 2-, ... digit numbers appearing are 0, 84, 504, 8580, 07010, 088880, ... (OEIS A000000), which end at digits 48, 934, 24437, 366399, 4910479, 49672582, ... (OEIS A000000).
It is known that the Copeland-Erdős constant is normal in base 10 (Copeland and Erdős 1946), though the following table giving the counts of digits in the first 
terms, shows non-normal behavior up to at least 
due arbitrarily cutting the digit string off in the middle of runs of primes with initial starting digits.
 |
OEIS |
10 |
100 |
 |
 |
 |
 |
 |
 |
 |
| 0 |
A000000 |
0 |
4 |
46 |
575 |
6799 |
75249 |
790407 |
8129359 |
83121745 |
| 1 |
A000000 |
4 |
33 |
266 |
2301 |
20468 |
187375 |
1766602 |
16794379 |
161034016 |
| 2 |
A000000 |
1 |
4 |
63 |
731 |
8016 |
84314 |
876083 |
9016914 |
91679602 |
| 3 |
A000000 |
2 |
16 |
134 |
1259 |
12015 |
115987 |
1134513 |
11201736 |
110467722 |
| 4 |
A000000 |
0 |
4 |
60 |
685 |
7286 |
76925 |
796194 |
8202026 |
83946253 |
| 5 |
A000000 |
1 |
5 |
58 |
674 |
7346 |
76886 |
794905 |
8161691 |
83863547 |
| 6 |
A000000 |
0 |
4 |
60 |
667 |
7247 |
76745 |
794002 |
8154232 |
83381734 |
| 7 |
A000000 |
2 |
16 |
133 |
1228 |
11889 |
115336 |
1129053 |
11107597 |
109702515 |
| 8 |
A000000 |
0 |
3 |
57 |
654 |
7107 |
76273 |
791955 |
8141173 |
83207903 |
| 9 |
A000000 |
0 |
11 |
123 |
1226 |
11827 |
114910 |
1126286 |
11090893 |
109594963 |
REFERENCES:
Copeland, A. H. and Erdős, P. "Note on Normal Numbers." Bull. Amer. Math. Soc. 52, 857-860, 1946.
Rodenkirch, M. "Copeland-Erdos Constant Primes." May. 5, 2016. https://www.mersenneforum.org/showthread.php?p=433145#post433145.
Sloane, N. J. A. Sequences A224897, A227530, and A229190 in "The On-Line Encyclopedia of Integer Sequences."
