Ramanujan calculated (Hardy 1999, Le Lionnais 1983, Berndt 1994), while the correct value is
(OEIS A070769; Derbyshire 2004, p. 114). The first decimal digits were computed by E. Weisstein on Oct. 7, 2013.
-constant primes occur for 4, 144, 227, 444, 19474, ... (OEIS A122422) decimal digits.
The Earls sequence (starting position of copies of the digit ) for is given for , 2, ... by 3, 42, 178, 10013, 31567, 600035, 1253449, ... (OEIS A229071).
The starting positions of the first occurrence of , 1, 2, ... in the decimal expansion of (not including the initial 0 to the left of the decimal point) are 17, 1, 8, 5, 2, 3, 6, 34, 11, ... (OEIS A229201).
Scanning the decimal expansion of until all -digit numbers have occurred, the last 1-, 2-, ... digit numbers appearing are 7, 465, 102, 5858, 48441, ... (OEIS A000000), which end at digits 34, 512, 7454, 92508, 1414058, ... (OEIS A000000).
The digit sequences 0123456789 and 9876543210 do not occur in the first digits (E. Weisstein, Oct. 7, 2013).
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 | 9 | 116 | 1053 | 10098 | 100104 | 999785 |
1 | A000000 | 1 | 7 | 100 | 970 | 9893 | 100238 | 1000370 |
2 | A000000 | 1 | 9 | 106 | 979 | 10113 | 100057 | 999594 |
3 | A000000 | 2 | 13 | 109 | 1012 | 10120 | 99999 | 1001006 |
4 | A000000 | 2 | 10 | 96 | 1019 | 10118 | 99822 | 999546 |
5 | A000000 | 1 | 15 | 103 | 994 | 9912 | 99918 | 1001007 |
6 | A000000 | 1 | 8 | 89 | 1036 | 10060 | 99971 | 999430 |
7 | A000000 | 0 | 6 | 97 | 988 | 10029 | 100141 | 997185 |
8 | A000000 | 1 | 15 | 101 | 988 | 9838 | 100089 | 1001593 |
9 | A000000 | 1 | 8 | 83 | 961 | 9819 | 99661 | 1000484 |