A concatenation sequence, or concatenated number sequence, is an integer sequence constructed by concatenating digits onto previous sequence terms.
Examples are summarized in the following table, with terms shown as digit strings that retain leading zeros. In each row, prefixing "0." to the infinite string gives the limiting constant, interpreted in base 2 for the binary row and base 10 otherwise. For the prime-counting construction, OEIS A366033 gives the successive digits of the limiting string.
| sequence | OEIS | limiting constant | terms |
| Smarandache numbers | A007908 | Champernowne constant | 1, 12, 123, 1234, 12345, 123456, ... |
| Smarandache-Wellin numbers | A019518 | Copeland-Erdős constant | 2, 23, 235, 2357, 235711, ... |
| concatenation of binary digits of positive integers | A058935 | binary Champernowne constant | 1, 110, 11011, 11011100, 11011100101, ... |
| concatenation of prime counting function values | prime-counting concatenation constant | 0, 01, 012, 0122, 01223, 012233, 0122334, ... |
