a(8) > 2*10^9.  Hiroaki Yamanouchi, Nov 29 2014
a(8) > 2*10^10.  Chai Wah Wu, Dec 07 2014
All terms of the sequence are even. a(5), a(6) and a(7) are of the form 2*p + 2 where p is a prime and mod(p, 14) = 1.  Farideh Firoozbakht, Dec 07 2014
From Jianing Song, Jan 13 2019: (Start)
Among the known terms only a(3) and a(4) are of the form 2*p where p is a prime.
a(n)^2 + 1 is prime for 2 <= n <= 7. Among these primes, the multiplicative order of 2 modulo a(n)^2 + 1 is 2*a(n) except for n = 5, in which case it is 2*a(n)/3. (End)
a(8) > 10^12.  Giovanni Resta, May 05 2020
