e Digits
The constant e with decimal expansion
(OEIS A001113) can be computed to 
digits of precision in 10 CPU-minutes on modern hardware.
was computed to 
digits by P. Demichel, and the first 
have been verified by X. Gourdon on Nov. 21, 1999 (Plouffe). 
was computed to 
decimal digits by S. Kondo on Jul. 5, 2010 (Yee).
The Earls sequence (starting position of 
copies of the digit 
) for 
is given for 
, 2, ... by 2, 252, 1361, 11806, 210482, 9030286, 3548262, 141850388, 1290227011, ... (OEIS A224828).
The starting positions of the first occurrence of 
in the decimal expansion of 
(including the initial 2 and counting it as the first digit) are 14, 3, 1, 18, 11, 12, 21, 2, ... (OEIS A088576).
Scanning the decimal expansion of 
until all 
-digit numbers have occurred, the last 1-, 2-, ... digit numbers appearing are 6, 12, 548, 1769, 92994, ... (OEIS A036900), which end at digits 21, 372, 8092, 102128, ... (OEIS A036904).
The digit sequence 0123456789 does not occur in the first 
digits of 
, but 9876543210 does, starting at position 
(E. Weisstein, Jul. 22, 2013).
-constant primes (i.e., e-primes) occur at 1, 3, 7, 85, 1781, 2780, 112280, 155025, ... (OEIS A64118) decimal digits.
It is not known if 
is normal, but the following table giving the counts of digits in the first 
terms shows that the decimal digits are very uniformly distributed up to at least 
.
 |
OEIS |
10 |
100 |
 |
 |
 |
 |
 |
 |
 |
 |
| 0 |
A000000 |
0 |
5 |
100 |
974 |
9885 |
99425 |
998678 |
9999138 |
100004425 |
1000024802 |
| 1 |
A000000 |
2 |
6 |
96 |
989 |
10264 |
100132 |
1000577 |
10004438 |
99982926 |
999989229 |
| 2 |
A000000 |
2 |
12 |
97 |
1004 |
9855 |
99845 |
999156 |
9998876 |
99999168 |
999997938 |
| 3 |
A000000 |
0 |
8 |
109 |
1008 |
10035 |
100228 |
1001716 |
10005176 |
100002498 |
999982936 |
| 4 |
A000000 |
1 |
11 |
100 |
982 |
10039 |
100389 |
1000307 |
9998285 |
100018922 |
1000026506 |
| 5 |
A000000 |
0 |
13 |
85 |
992 |
10034 |
100087 |
999903 |
9998042 |
100003884 |
999967300 |
| 6 |
A000000 |
0 |
12 |
99 |
1079 |
10183 |
100479 |
998869 |
10000158 |
99987241 |
999931170 |
| 7 |
A000000 |
1 |
16 |
99 |
1008 |
9875 |
99910 |
1000813 |
9998342 |
99997536 |
1000013049 |
| 8 |
A000000 |
4 |
7 |
103 |
996 |
9967 |
99814 |
999703 |
10000336 |
100005348 |
1000074277 |
| 9 |
A000000 |
0 |
10 |
112 |
968 |
9863 |
99691 |
1000278 |
9997209 |
99998052 |
999992793 |
REFERENCES:
Sloane, N. J. A. Sequences A001113/M1727, A036900, A036904, A064118, A088576, and A224828 in "The On-Line Encyclopedia of Integer Sequences."
Yee, A. J. "y-cruncher - A Multi-Threaded Pi-Program." http://www.numberworld.org/y-cruncher/.
