Name of this recursively defined sequence of prime numbers?

Question

I was wondering if the following sequence has a name:

Let $P$ be the set of prime numbers, and $p: \mathbb{N} \rightarrow P$ be the (increasing) enumerating function of the set.

Let's define $\alpha_1 = 2, \alpha_{n+1} = p(\alpha_n)$, i.e.,the $\alpha_n-$prime number.

Is there a name for this sequence? The first terms are $2,3,5,11,...$

I know they code one-branch-trees in the Cappello (non standard) codification of rooted trees. (in fact that's why I'm interested in them)

Answer 1

You can find the sequence on OEIS here (A00707097). The name given is "Primeth recurrence".