Numbers n such that (5*2^n - 1)/3 is prime.
1, 3, 5, 9, 11, 17, 21, 23, 41, 65, 81, 263, 515, 527, 701, 897, 1269, 1451, 1607, 1665, 3539, 4727, 5097, 7089, 9017, 9809, 10989, 20229
1
For even n these numbers are fractions. Hence, these are the primes in sequence (10*4^n-1)/3. These n form the numbers given in S000443.
T. D. Noe, Plot of 28 terms
(Mma) Select[Range[5000], PrimeQ[(10*4^# - 1)/3]&]
nonn,hard,more
T. D. Noe, Jan 08 2015