First 6 terms generated on applying the simple rule are displayed here.
5, 8, 18, 102, 322, 1830, ?, ?, ?
Hint 1:
The number series used to generate the sequence is itself a subset of more well known series.
Hint 2:
More well known series is the sequence of Prime Numbers.
Hint 3:
Subset of Primes is Fibonacci Primes.