The OEIS, a collection that was begun by Neil J. A. Sloane, is an online databse of over $360,000$ integer sequences. Now, suppose I have an integer sequence, say, $a_1, a_2, a_3, ...$ I look for this sequence in OEIS. The sequence is unavailable.
Maybe there are two sequences in OEIS such that my sequence is a sum of those two sequences.
How can I search if my sequence is a sum of two sequences in OEIS?
The OEIS has a feature called "Superseeker" that is supposed to do just this sort of thing.
Also, as Idéophage suggests, you can download the database to your computer and write a program that checks if your sequence is the sum of any existing sequences.