The best description of the OEIS I've heard is by Donald Knuth in this fun talk (https://youtu.be/BxQw4CdxLr8) where at 19:50 he says how it lets you "compute your way into the literature":
> For the last 30 years or more, there has been a wonderful tool for all kinds of problems of this form and it's been online for a long time: we have the Online Encyclopedia of Integer Sequences. And this is just the nicest thing since sliced bread for mathematics because you can compute your way into the literature. [audience laughter] If you want to know if anybody else has ever studied a problem, all you have to do is evaluate the first few cases of it and then you look it up and there it is. The hit rate is incredible, and all kinds of mathematicians have discovered each other through the OEIS. […] I donate to Wikipedia and the Internet Archive and the OEIS.
Indeed I've used it this way many times; the most recent example is that I became curious about how many polynomial functions there are mod n (after posting this comment: https://news.ycombinator.com/item?id=26482028), and by computing the answers for n up to 10, I was able to look up up those numbers in the OEIS and find the general formula, and also the relevant papers. (Asked a question about it here: https://math.stackexchange.com/questions/4070051/how-many-di... but ended up answering it myself…) I don't think I'd have even known where to look (as I'm not a professional mathematician), if not for the OEIS. And this happens again and again.
Always great. A fine technique to compensate for those of us who lack mathematical sophistication: write some godawful brute force code to calculate the number of items in some construct of interest, then search those numbers up to learn all sorts of useful new things about what you have.
I learned about generalizations of the Fibonacci sequence and "half-Catalan numbers" by this method.
It's an interesting and useful project. Any time you have a thing you don't understand it's worth finding some way of converting it to an integer sequence and then looking it up, just in case.
I like how everybody here uses this website for some profound mathematical purposes, but I once won a cordless drill due to the OEIS in high school. At some hackathon Bosh had a booth with a contest where you had to solve puzzles which consiststed mainly of finishing integer sequences. I remembered this encyclopedia and I found all of them on the oeis.
Thanks for this link. I am working on a superoptimizer and once had the thought that OEIS would be a cool place to look for workloads. It's gratifying that someone else is doing this and having some success.
As far as I can tell its assembly language is designed for fast synthesis and check (e.g. all programs are known to terminate). There is a "miner" generating programs and checking against existing sequences 24/7, a Twitter bot is also available [1].
The OEIS is an amazing tool. I recently came across a sequence from an unusual source and then made the shocking discovery that the sequence already existed. It turned out to be a wild coincidence.
The OEIS can also be considered a sort of number encyclopedia, especially for large numbers.
It can also be interesting to link geometric observations with unrelated OEIS sequences. For example, the number of rectangles on a square grid turned out to be the octagonal pyramidal numbers.
I love this site. Often if I solve a Project Euler problem of the form "what is the xth element...", after I solve it, I will look at the first several elements in the sequence and start seeing where else the sequence is used.
There're few times some well-known sequences have appeared in AoC. Examples are Manhattan distances (OEIS:A214526) and square sums spiral (OEIS:A141481) in 2017d3, tribonacci (OEIS:A000073) in 2020d10, and Van Eck's sequence (OEIS:A181391) in 2020d15.
> For the last 30 years or more, there has been a wonderful tool for all kinds of problems of this form and it's been online for a long time: we have the Online Encyclopedia of Integer Sequences. And this is just the nicest thing since sliced bread for mathematics because you can compute your way into the literature. [audience laughter] If you want to know if anybody else has ever studied a problem, all you have to do is evaluate the first few cases of it and then you look it up and there it is. The hit rate is incredible, and all kinds of mathematicians have discovered each other through the OEIS. […] I donate to Wikipedia and the Internet Archive and the OEIS.
(Aside: A good blog post about that lecture: https://thenewstack.io/donald-knuths-christmas-tree-lecture-...)
Indeed I've used it this way many times; the most recent example is that I became curious about how many polynomial functions there are mod n (after posting this comment: https://news.ycombinator.com/item?id=26482028), and by computing the answers for n up to 10, I was able to look up up those numbers in the OEIS and find the general formula, and also the relevant papers. (Asked a question about it here: https://math.stackexchange.com/questions/4070051/how-many-di... but ended up answering it myself…) I don't think I'd have even known where to look (as I'm not a professional mathematician), if not for the OEIS. And this happens again and again.