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Old 2017-03-17, 01:32   #8
CRGreathouse's Avatar
Aug 2006

597910 Posts

Originally Posted by carpetpool View Post
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.

Originally Posted by carpetpool View Post
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^n-1 (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^n-1 is prime for?
I don't know. This sequence grows slower than 2^n-1, with its main term being 1.9318516...^n, but it really comes down to its behavior on small prime factors.
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