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."