Are A014692 and A086969 the same sequence?

[Jonathan Post]

Okay, Ray: want to generalize to

Number of primes between p(p(n)) and p(p(p(n))) inclusive;
Number of primes between p(p(p(n))) and p(p(p(p(n)))) inclusive;
Number of primes between p(p(p(p(n)))) and p(p(p(p(p(n))))) inclusive?

In this context, I dare not speak the [keyword: less] word "k-almost prime..."



This isn't the biggest math question facing me (or humanity) at the 
moment, but I am wondering...

What is the sequence where n is included if F(n^2) is a multiple of 
F(n)^2, where F(n) is the nth Fibonacci number?

(I say "F(n^2) is a multiple of F(n)^2" instead of "F(n)^2 divides 
F(n^2)" so as to include the n=0 case.)

I get the sequence beginning 0,1,2,5,... (and then my calculator runs out 
of digits).

These terms (0 excluded) are too few to do any meaningful search on the 
EIS. Is this sequence already in the EIS? I bet it is, but under a 
different name.

Or maybe the sequence is finite.

Thanks,
Leroy Quet