Source: Quanta Magazine, Aug 2015
the Online Encyclopedia of Integer Sequences (OEIS), often simply called “Sloane” by its users.
This giant repository, which celebrated its 50th anniversary last year, contains more than a quarter of a million different sequences of numbers that arise in different mathematical contexts, such as the prime numbers (2, 3, 5, 7, 11 … ) or the Fibonacci sequence (0, 1, 1, 2, 3, 5, 8, 13 … ). What’s the greatest number of cake slices that can be made with n cuts? Look up sequence A000125 in the OEIS. How many chess positions can be created in n moves? That’s sequence A048987. The number of ways to arrange n circles in a plane, with only two crossing at any given point, is A250001. That sequence just joined the collection a few months ago. So far, only its first four terms are known; if you can figure out the fifth, Sloane will want to hear from you.
A mathematician whose research generates a sequence of numbers can turn to the OEIS to discover other contexts in which the sequence arises and any papers that discuss it. The repository has spawned countless mathematical discoveries and has been cited more than 4,000 times.
Are there other repositories of mathematical information that you wish existed, but don’t yet?
You would like an index to theorems, but it’s hard to imagine how that would work.
We’re trying to get a collaboration going with the Zentralblatt — the German equivalent of Math Reviews’ MathSciNet — about making it possible to search for formulas in the OEIS. Suppose you want the summation of xn over n2 + 3, where the sum goes from one to infinity. It’s very hard to look that up in the OEIS at present.