The digits of the natural logarithm of 2 are those of its decimal expansion
 |
(OEIS A002162). It was computed to 
decimal digits by S. Kondo
on May 14, 2011 (Yee).
The Earls sequence (starting position of 
copies of the digit 
) for 
is given for 
, 2, ... by 4, 419, 2114, 3929, 38451, 716837, 6180096, 10680693,
2539803904 (OEIS A228242).
-constant primes occur at 321, 466, 1271, 15690, 18872,
89973, ... decimal digits (OEIS A228226).
The starting positions of the first occurrence of 
, 1, ... in the decimal
expansion of 
are 9, 4, 22, 3, 5, 10, 1, 6, 8, ... (OEIS A100077).
Scanning the decimal expansion of 
until all 
-digit strings, including those with
leading zeros, have occurred, the last 1-, 2-, ...-digit
strings appearing are 2, 98, 604, 1155, 46847, 175403, ... (OEIS A036901),
which end at digits 22, 444, 7655, 98370, 1107795, 12983306,
... (OEIS A036905).
The digit string 0123456789 occurs starting at positions 3157027485, 8102152328, ... in the decimal digits of 
,
and 9876543210 occurs starting at position 380113805, with no other occurrences in
the first 
digits (E. Weisstein, Aug. 20, 2013).
It is not known if 
is normal.
