For large n, these numbers can be closely approximated by the number of primes < (3^n)^2. For example, the sum of primes < 3^12 = 11150031169. The number of primes < (3^12)^2 = 3^24 = 11152818693. The error here 0.000250.

The second term, 5 is the addition of the primes 2 and 3 since we defined the sequence as less than or equal.