The decimal digits of the Glaisher-Kinkelin constant begin
(OEIS A074962). was computed to
decimal digits by E. Weisstein
(Dec. 3, 2015).
The Earls sequence for gives the starting position of the first string
formed by
copies of the decimal representation of
, counting from 1 after the decimal
point. Its first terms, for
,
2, ..., are 7, 14, 2264, 1179, 411556, ... (OEIS A225763).
A scan reported no occurrence of the strings 0123456789 and 9876543210 in the first decimal digits
(E. Weisstein, Dec. 3, 2015).
The lengths of -constant primes, formed
by concatenation of initial decimal
digits of
including the integer part, begin 7, 10, 18, 64, 71, 527,
1992, 5644, 8813, 19692, ... (OEIS A118420).
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 decimal
digit) are 12, 1, 2, 18, 5, 22, 14, 7, 3, 10, ... (OEIS A229193).
Scanning the decimal expansion of until all strings of
decimal digits have occurred,
including those with leading zeros, the last 1-, 2-, ... digit strings appearing are 5, 98, 478, 9192, ..., which end at
digits 22, 495, 7233, 100426, ..., counting the initial
1 as the first decimal digit.
It is not known if the Glaisher-Kinkelin constant is normal in base
10. The following table gives reported counts of each decimal
digit in the first fractional decimal digits
for
, 2, ..., 5.
| OEIS | 10 | 100 | ||||
| 0 | 0 | 11 | 96 | 999 | 9890 | |
| 1 | 2 | 9 | 102 | 1033 | 9928 | |
| 2 | 4 | 16 | 93 | 992 | 9977 | |
| 3 | 0 | 8 | 100 | 1016 | 10055 | |
| 4 | 1 | 8 | 99 | 955 | 10043 | |
| 5 | 0 | 5 | 94 | 979 | 10034 | |
| 6 | 0 | 12 | 96 | 988 | 10121 | |
| 7 | 1 | 12 | 114 | 1067 | 9998 | |
| 8 | 1 | 11 | 108 | 1031 | 9999 | |
| 9 | 1 | 8 | 98 | 940 | 9955 |