Definition:Computable Rational Sequence

Definition

Let $\sequence {x_n}_{n \in \N}$ be a infinite sequence of rational numbers.

Then, $\sequence {x_n}$ is a computable rational sequence if and only if there exist total recursive functions $f, g : \N \to \N$ such that, for all $n \in \N$:

$x_n = \dfrac {k_n} {\map g n + 1}$

where $\map f n$ codes the integer $k_n$.

Sources

• This article incorporates material from computable sequence on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.