Pythagoras's constant digits are the digits of Pythagoras's constant, whose decimal expansion is
 |
(OEIS A002193). It was computed to 
decimal digits by A. J. Yee
on Feb. 9, 2012.
The Earls sequence (starting position of 
copies of the decimal representation
of 
,
counting from the first digit after the decimal
point) for 
is given for 
, 2, ... by 2, 114, 1481, 3308, 72459, 226697, 969836, 119555442,
2971094743, ... (OEIS A224871).
-constant primes occur at 55, 97, 225, 11260, 11540,
... (OEIS A115377) decimal digits,
including the initial integer-part 1.
The starting positions of the first occurrence of 
, 1, 2, ... in the decimal
expansion of 
(including the initial 1 and counting it as the first
digit) are 14, 1, 5, 7, 2, 8, 9, 12, 19, ... (OEIS A229199).
Scanning the decimal expansion of 
, including the initial integer-part 1, until all 
-digit strings have occurred, including
those with leading zeros, the last 1-, 2-, ...-digit strings appearing are 8, 81, 748, 8505, 30103, 489568, ...,
which end at digits 19, 420, 8326, 94388, 1256460, 13043524,
....
The digit sequence 9876543210 does not occur in the first 
digits of 
, but 0123456789 does, starting at positions 864106288,
6458611884, 7311432557, ... (E. Weisstein, Jul. 22, 2013).
It is not known if 
is normal (Beyer et
al. 1969, 1970a,b), but the following table giving the counts of digits
in the first 
digits after the decimal
point shows that the decimal digits are very uniformly
distributed up to at least 
.
 | OEIS | 10 | 100 |  |  |  |  |  |  |  |  |
| 0 | 0 | 10 | 108 | 952 | 9959 | 99814 | 999897 | 10002237 | 100010228 | 999996989 | |
| 1 | 2 | 7 | 98 | 1005 | 10106 | 98924 | 1000114 | 10000179 | 99998381 | 1000042849 | |
| 2 | 2 | 8 | 109 | 1004 | 9876 | 100436 | 1000208 | 9998091 | 99995645 | 999987069 | |
| 3 | 2 | 11 | 82 | 980 | 10058 | 100191 | 999674 | 10004178 | 99995415 | 999984900 | |
| 4 | 2 | 9 | 100 | 1016 | 10100 | 100024 | 1000126 | 10000054 | 100012725 | 1000008724 | |
| 5 | 1 | 7 | 104 | 1001 | 10002 | 100155 | 999358 | 9998344 | 100002636 | 999970045 | |
| 6 | 1 | 10 | 90 | 1032 | 9939 | 99886 | 1001246 | 10001665 | 100012683 | 1000007824 | |
| 7 | 0 | 18 | 104 | 964 | 10008 | 100008 | 999359 | 9998646 | 99980315 | 999986743 | |
| 8 | 0 | 12 | 113 | 1027 | 10007 | 100441 | 999452 | 9996550 | 99995120 | 1000025363 | |
| 9 | 0 | 8 | 92 | 1019 | 9945 | 100121 | 1000566 | 10000056 | 99996852 | 999989494 |
