Constant digit scanning consists of scanning the decimal expansion of a positive constant
until all 
-digit strings have been seen, where
is a positive integer. The strings
may overlap and include leading zeros. The decimal point
and an initial 0 to its left are omitted.
The following table gives the number of digits that must be scanned to encounter all 
, 2, ...-digit strings,
together with the last 
-digit string
encountered. The scan count is the ending position of that string.
For each constant, the first row lists scan counts and
the second row, when present, lists last strings. Last
strings are read as having 
digits, adding leading zeros when
necessary.
| constant | OEIS | sequence |
| Apéry's constant | A036906 | 23, 457, 7839, 83054, 1256587, 13881136, 166670757, ... |
| A036902 | 7, 89, 211, 2861, 43983, 292702, 8261623, ... | |
| Catalan's constant | 32, 716, 7700, 86482, 1143572, ... | |
| 8, 45, 529, 2679, 24200, ... | ||
| Champernowne constant | A072290 | 11, 192, 2893, 38894, 488895, 5888896, 68888897, 788888898, 8888888899, ... |
| Copeland-Erdős constant | 48, 934, 24437, 366399, 4910479, 49672582, ... | |
| 0, 84, 504, 8580, 07010, 088880, ... | ||
| e | A036904 | 21, 372, 8092, 102128, 1061613, 12108841, 198150341, 1929504534, ... |
| A036900 | 6, 12, 548, 1769, 92994, 513311, 1934715, 56891305, ... | |
| Euler-Mascheroni constant | 16, 658, 6600, 91101, 1384372, ... | |
| 8, 18, 346, 2778, 84514, ... | ||
| Glaisher-Kinkelin constant | 22, 495, 8268, ... | |
| 5, 98, 478, ... | ||
| golden ratio | 23, 770, 5819, 93910, 1154766, 13192647, ... | |
| 5, 55, 515, 0092, 67799, 290503, ... | ||
| Golomb-Dickman constant | 28, 587, 6322, ... | |
| 1, 33, 821, ... | ||
| Khinchin's constant | 23, 499, 8254, ... | |
| 7, 43, 782, ... | ||
| natural logarithm of 2 | A036905 | 22, 444, 7655, 98370, 1107795, 12983306, ... |
| A036901 | 2, 98, 604, 1155, 46847, 175403, ... | |
| natural logarithm of 10 | A229124 | 22, 701, 7486, 88092, 1189434, 13426407, ... |
| A229126 | 7, 38, 351, 8493, 33058, 362945, ... | |
| pi | A080597 | 33, 607, 8556, 99850, 1369565, 14118313, 166100507, 1816743913, 22445207407, 241641121049, 2512258603208, ... |
| A032510 | 0, 68, 483, 6716, 33394, 569540, 1075656, 36432643, 172484538, 5918289042, 56377726040, ... | |
| Pythagoras's constant | 19, 420, 8326, 94388, 1256460, 13043524, ... | |
| 8, 81, 748, 8505, 30103, 489568, ... | ||
| Soldner's constant | 34, 512, 7454, 92508, ... | |
| 7, 46, 102, 5858, ... | ||
| Theodorus's constant | 23, 378, 7862, 77437, 1237533, 16362668, ... | |
| 4, 91, 184, 5566, 86134, 35343, ... |
The starting positions of the first occurrence of the unpadded decimal representations of 
,
1, 2, ... in the decimal expansion of a number
of constants are summarized in the table below.
| constant | OEIS | first occurrence of 0, 1, 2, ... |
| Apéry's constant | A229187 | 3, 1, 2, 10, 16, 6, 7, 23, 18, 8, ... |
| Catalan's constant | A100079 | 16, 2, 13, 24, 9, 3, 5, 11, 32, 1, ... |
| Champernowne constant | A229186 | 11, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ... |
| Copeland-Erdős constant | A229190 | 48, 5, 1, 2, 21, 3, 31, 4, 41, 12, ... |
| e | A088576 | 14, 3, 1, 18, 11, 12, 21, 2, 4, 13, ... |
| Euler-Mascheroni constant | A229192 | 11, 5, 4, 14, 9, 1, 7, 2, 16, 10, 36, ... |
| Glaisher-Kinkelin constant | A229193 | 12, 1, 2, 18, 5, 22, 14, 7, 3, 10, 11, ... |
| Golomb-Dickman constant | A229195 | 15, 28, 2, 4, 3, 10, 1, 17, 8, 6, 28, ... |
| golden ratio | A088577 | 5, 1, 20, 6, 12, 23, 2, 11, 4, 8, 232, ... |
| Khinchin's constant | A229196 | 8, 10, 1, 14, 5, 4, 2, 23, 3, 22, 10, ... |
| natural logarithm of 2 | A100077 | 9, 4, 22, 3, 5, 10, 1, 6, 8, 2, 108, ... |
| natural logarithm of 10 | A229197 | 3, 21, 1, 2, 13, 5, 17, 22, 6, 9, 41, ... |
| pi | A032445 | 33, 2, 7, 1, 3, 5, 8, 14, 12, 6, 50, ... |
| Pythagoras's constant | A229199 | 14, 1, 5, 7, 2, 8, 9, 12, 19, 15, 77, ... |
| Soldner's constant | A229201 | 17, 1, 8, 5, 2, 3, 6, 34, 11, 7, 16, ... |
| Theodorus's constant | A229200 | 5, 1, 4, 3, 23, 6, 12, 2, 8, 18, 48, ... |
