Advanced software for OEIS?

There is a "superseeker" option at OEIS which does something like what you are asking for.

Perhaps worth mentioning here Sagemath's functionality to communicate with OEIS. (Sagemath is basically a large Python library).

Apart from searching, one can retrieve components of records, etc etc.

Another way to interact with OEIS in Sagemath is via FindStat, see here.

There is also a Haskell package with similar functionality.

There has been some previous discussion on the OEIS mailing list about similar topics. For instance, about the sum of two sequences. (If I recall correctly, there was a university project that performed a more in depth search to find new combinations for existing sequences, but I can't seem to find the details now...).

For more of an answer to your question, I would check out this thread: http://list.seqfan.eu/pipermail/seqfan/2015-February/014455.html where a user links to some code (on github) which is currently implemented on a website http://www.sequenceboss.org/ (was a bit slow on first load for me).

Plugging in the above numbers gives me:

---

Result
SequenceBoss thinks the sequence

$$(a_n)_{n≥1}=2,4,9,16,27,38,…$$ is generated by

$$a_n=(−1+n)^2+\text{prime}(n)$$ If true, the sequence continues

$$2,4,9,16,27,38,53,68,87,110,131,…$$

http://sequenceboss.org/?q=2%2C+4%2C+9%2C+16%2C+27%2C+38