Is there (if not, why?) a software where I can input a sequence of integers, like into the OEIS, and then it makes some simple transformations on it to check whether the sequence can be obtained from some other sequence(s)?
For example, if I enter 2, 4, 6, 8, 10, then currently OEIS returns A005843: The nonnegative even numbers (which starts with 0, but OEIS can search for subsequences).
But suppose that A005843 is not in the database yet.
Then OEIS will not return anything.
Instead, a more intelligent search software could return A000027: The positive integers.
I know that this raises several questions, like what transformations, which sequences to display first etc., but the feature could be quite useful.
Even better, if the software could do more complicated things, like check whether my sequence is the sum of two OEIS entries.
ps. My motivation came from the sequence 2, 4, 9, 16, 27, 38 currently missing from OEIS, which was posed on this Hungarian puzzle page.
(The puzzle has already expired, so feel free to discuss.)
Best Answer
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