The decimal digits of the golden ratio begin
 |
(OEIS A001622). A computation to 
digits of precision
was reported to take 24 CPU-minutes. Yee reports a computation of 
to 
decimal digits completed
on Jul. 8, 2010.
The Earls sequence for 
gives the starting positions of 
consecutive copies of the decimal representation of 
, counting from 1 after the decimal
point. For 
,
2, ..., it begins 2, 62, 158, 1216, 72618, 2905357, 7446157, 41398949, 1574998166,
... (OEIS A224844).
The digit sequence 0123456789 does not occur in the first 
digits of 
, but 9876543210 does, starting at position 
(E. Weisstein, Jul. 22, 2013).
Phi-primes, i.e., 
-constant primes occur
for 7, 13, 255, 280, 97241, ... (OEIS A064119)
decimal digits.
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 5, 1, 20, 6, 12, 23, 2, 11, 4, 8, 232, ... (OEIS A088577).
Scanning the decimal expansion of 
, including its initial 1, until all strings
of 
decimal digits have occurred, the last strings of lengths
1, 2, ... appearing are 5, 55, 515, 0092, 67799, 290503, ..., which end at positions
23, 770, 5819, 93910, 1154766, 13192647, ....
It is not known if 
is normal in base 10. The
following table gives reported counts of each decimal
digit 
in the first 
decimal digits after the decimal
point, for 
,
2, ..., 10.
 | OEIS | 10 | 100 |  |  |  |  |  |  |  |  |
| 0 | 1 | 11 | 100 | 1020 | 9986 | 99805 | 1001143 | 10003332 | 100007840 | 1000031042 | |
| 1 | 1 | 9 | 105 | 1062 | 9963 | 99993 | 1000118 | 10000255 | 99999864 | 999990982 | |
| 2 | 0 | 11 | 116 | 994 | 9950 | 99529 | 1000776 | 10002116 | 100002106 | 1000005392 | |
| 3 | 2 | 9 | 88 | 1039 | 10079 | 99833 | 999794 | 9999184 | 99979352 | 999978183 | |
| 4 | 0 | 12 | 92 | 976 | 10041 | 100151 | 999367 | 9998797 | 99995481 | 999952470 | |
| 5 | 0 | 5 | 84 | 988 | 10016 | 100067 | 999725 | 9996151 | 99999934 | 1000032985 | |
| 6 | 1 | 9 | 104 | 918 | 9975 | 100328 | 999455 | 9996149 | 100004208 | 1000014191 | |
| 7 | 1 | 10 | 113 | 1025 | 9988 | 100160 | 1000852 | 9997524 | 100018237 | 1000023870 | |
| 8 | 3 | 15 | 105 | 987 | 10008 | 100236 | 1000059 | 10005419 | 99995223 | 999976728 | |
| 9 | 1 | 9 | 93 | 991 | 9994 | 99898 | 998711 | 10001073 | 99997755 | 999994157 |
