“OEIS: A Handbook of Integer Sequences 50 Years Later”, 2023-01-09 (; backlinks):
[media] Until 1973 there was no database of integer sequences. Someone coming across the sequence 1, 2, 4, 9, 21, 51, 127, …, would have had no way of discovering that it had been studied since 1870 (today these are called the Motzkin numbers, and form entry A001006 in the database). Everything changed in 1973 with the publication of A Handbook of Integer Sequences, which listed 2,372 entries.
This report describes the 50-year evolution of the database from the Handbook to its present form as “The On-Line Encyclopedia of Integer Sequences” (or OEIS), which contains 360,000 entries, receives a million visits a day, and has been cited 10,000×, often with a comment saying “discovered thanks to the OEIS”.
…I could have chosen a simpler example, like the Fibonacci numbers, but I have a particular reason for choosing the Catalan numbers. When the OEIS was new, people would sometimes say to me that they had a sequence they were trying to understand, and would I show them how to use the database. At least twice when I used the Catalan sequence as an illustration, they said, “why, that is my sequence, how on earth did you know?” It was no mind-reading trick, the Catalan numbers are certainly the most common sequence that people don’t know about. This entry is the longest—and one of the most important—in the whole database.
If we do not find your sequence in the database, we will send you a message inviting you to submit it (if you consider it is of general interest), so that the next person who comes across it will be helped, and your name will go on record as the person who submitted it.
The second main use of the database is to find out the latest information about a particular sequence.
Of course we cannot hope to keep all 360,000 entries up-to-date. But when a new paper is published that mentions the OEIS, Google will tell us, and we then add links to that paper from any sequence that it mentions. People have told us that this is one of the main ways they use the OEIS. After all, even a specialist in (say) permutation groups cannot keep track of all the papers published worldwide in that area. And if a paper in a physics journal happens to mention a number-theoretic sequence, for example, that is unlikely to be noticed by mathematicians.
…A less-obvious use of the database is to quickly tell you how hard a problem is. I use it myself in this way all the time. ‘Is the sequence “Catalan” or “Collatz”?’ If a sequence comes up in your own work, or when reviewing someone else’s work, it is useful to know right away if this is a well-understood sequence, like the Catalan numbers, or if it is one of the notoriously intractable problems like the Collatz or 3x + 1 problem (A006577).