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Integer Sequences

An integer sequence can be explicit or implicit.
Explicit: a formula is used to create the next term, for example 2n+8. The number after 5 would be 18 (2x5+8).
Implicit: a relationship between the terms give the next term. For example: adding the two last terms to give the next.

The members of a sequence can also have certain properties that other numbers don't. For example Prime numbers, which are only divisible by 1 and themself.

Examples of sequences (from Wikipedia)