Inverse function of A006450; primes in it; inverse function of primeth recurrence

[Jonathan Post]

Am I right that OEIS does not yet have the inverse function of
A006450?  Just as pi(n) is the inverse function of prime(n), so also
is pi(pi(n)) = A000720(A000720(n)) the inverse function of
prime(prime(n)) = A000040(A000040(n)).

pi(pi(n)) begins I think:

1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 5

It is a step function, increasing by 1 precisely for those n which are
values of pi(n).

This also gives us the once-iterated analogue of A048989 pi(n) is
prime, namely the new seq pi(pi(n)) is prime:
5,6,7,8,9,10,11,12,13,14,15,16,31,32,33,34,35,36,37,38,39,40,59, 60, ...

We likewise a well-defined inverse function to the nice njas/rgwv
A007097  Primeth recurrence: a(n+1) = a(n)-th prime.

Are these worth submitting when vacation ends?

I considered this when Robert G. Wilson v and I worked on
A101184 a(n) = n + pi(n) + pi(pi(n)) + pi(pi(pi(n))) + pi(pi(pi(pi(n)))) + ...