For questions related to integer sequences (i.e. an ordered list of integers).
An integer sequence may be specified explicitly by giving a formula for its $n$th term, or implicitly by giving a relationship between its terms. For example, the sequence $0, 1, 1, 2, 3, 5, 8, 13,\dots$ (the Fibonacci sequence) is formed by starting with $0$ and $1$ and then adding any two consecutive terms to obtain the next one: an implicit description. The sequence $0, 3, 8, 15, \dots$ is formed according to the formula $n^2 − 1$ for the $n$th term: an explicit definition.
Alternatively, an integer sequence may be defined by a property which members of the sequence possess and other integers do not possess. For example, we can determine whether a given integer is a perfect number, even though we do not have a formula for the $n$th perfect number.
An integer sequence is a computable sequence if there exists an algorithm which, given $n$, calculates $a_n$, for all $n > 0$. The set of computable integer sequences is countable. The set of all integer sequences is uncountable (with cardinality equal to that of the continuum), and so not all integer sequences are computable.
Although some integer sequences have definitions, there is no systematic way to define what it means for an integer sequence to be definable in the universe or in any absolute (model independent) sense.
