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)


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

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