Quote:
Originally Posted by carpetpool
Thanks, CRGreathouse for those terms. To make sure (so an OEIS sequence can be added), are these the correct indices n (for a(n)) in order up to n = 20k?

I wasn't making that claim, but it happens to be true as the next two are 27947 and 34351.
Quote:
Originally Posted by carpetpool
Also just for curiosity, what is the density for the prime indices n such that a(n) is prime for compared to the primes n such that 2^n1 (Mersenne) is prime for?
In other words, for any prime n, what is the (approximate) probability that a(n) is prime for, and for any given prime n, is there a greater chance that a(n) or 2^n1 is prime for?

I don't know. This sequence grows slower than 2^n1, with its main term being 1.9318516...^n, but it really comes down to its behavior on small prime factors.