n such that (3^n+1)/2 is prime: 1, 2, 4, 16, 32, 64.
Primes can only occur for n=2^k. - Don Reble (djr(AT)nk.ca), April 28 2004. The next term (if it exists) has k>=21 (i.e. more than 10^6 decimal digits).
EXAMPLE
a(3)=41 because it can be written as (3^4+1)/2=82/2.