# Simple Rule Generates this Sequence from Well Known Number Series

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.

• Is this the sum/product/difference of two well known number series? – Weather Vane May 28 at 19:41
• I did not mention 2.....not to be found in oeis....numbers are derived from this series...this concept hasn’t been introduced in none of my puzzles so far..series will become fairly big after ten more terms – Uvc May 28 at 20:48
• Sorry: "Well Known Number Series" does not contain any article so I can't tell whether "series" is singular or plural. – Weather Vane May 28 at 20:50
• It is a singular series. – Uvc May 28 at 20:51
• I will drop some hints to help. Today I am posting Hint 1. – Uvc May 29 at 13:28

Since no answer was posted so far, in spite of hints, I am posting an answer. In general, most of my sequences won’t be found in OEIS. They are generated using simple rules based on widely known sequences and they can be regenerated without calculators and computers. They have several practical applications in security and cryptography.

Series:

Well known Fibonacci Prime Series
$$2, 3, 5, 13, 89, 233, 1597, 28657, 514229.......$$

Rule:

Sum each Successive Pair

Final Series:

$$5, 8, 18, 102, 322, 1830, 30254, 542886....$$