Definition:Sequence Coding

Let $$\left \langle {a_1, a_2, \ldots, a_k}\right \rangle$$ be a finite sequence in $$\N^*$$ (that is, $$\forall i \in \left\{{1, 2, \ldots, k}\right\}: a_i > 0$$).

Let $$p_i$$ be the $$i$$th prime number, so that:
 * $$p_1 = 2$$;
 * $$p_2 = 3$$;
 * $$p_3 = 5$$;
 * $$p_4 = 7$$, etc.

Let $$n = p_1^{a_1} p_2^{a_2} \cdots p_k^{a_k}$$ where $$p_i$$ is the $$i$$th prime number.

Then $$n \in \N$$ codes the sequence $$\left \langle {a_1, a_2, \ldots, a_k}\right \rangle$$, or $$n$$ is the code number for the sequence $$\left \langle {a_1, a_2, \ldots, a_k}\right \rangle$$.

The set of all code numbers of finite sequences in $$\N$$ is denoted $$\operatorname{Seq}$$.

Note that $$n \in \operatorname{Seq}$$ iff $$n$$ is divisible by all the primes $$p_1, p_2, \ldots, p_k$$, where $$p_k$$ is the largest prime dividing $$n$$.