> My fascination with these sequences began in 1964 when I was a graduate student at Cornell University in Ithaca, NY, studying neural networks. I had encountered a sequence of numbers, 1,8,78,944,13800,..., and I badly needed a formula for the n-th term, in order to determine the rate of growth of the terms (this would indicate how long the activity in this very simple neural network would persist). I will say more about this sequence in Section 2.1.<p>It’s really fascinating to bump into mentions of NNs from the 60s & 70s. They seems to be quite hot at the time. The paper on the Medial Axis Transform mentions neural networks too, in a way that makes it seem like it was the cool thing to do. By the time I was in college, NNs were very out of fashion.<p>Here’s the NN problem Neil was working on, and the first sequence in the database: <a href="https://oeis.org/A000435" rel="nofollow">https://oeis.org/A000435</a>
Neil Sloane (author of the paper and curator of the OEIS) has been featured on Numberphile several times and it’s always a pleasure to watch. <a href="https://m.youtube.com/playlist?list=PLt5AfwLFPxWJXQqPe_llzWmTHMPb9QvV2">https://m.youtube.com/playlist?list=PLt5AfwLFPxWJXQqPe_llzWm...</a>
This makes me so happy to read. I had the privilege of working on the same lab as Neil (and Dave Applegate, another notable person in OEIS). No exaggeration at all to call them geniuses, you hang out with them for 5 minutes and know they're cut from different cloth. Nicest folk, too.
>"My fascination with these sequences began in 1964 when I was a graduate student at Cornell University in Ithaca, NY, studying neural networks. I had encountered a sequence of numbers, 1, 8, 78, 944, 13800, . . ., and I badly needed a formula for the n-th term, in order to determine the rate of growth of the terms..."<p>Related Mathologer video:<p>Mathologer - "Why don't they teach Newton's calculus of 'What comes next?'"<p><a href="https://www.youtube.com/watch?v=4AuV93LOPcE">https://www.youtube.com/watch?v=4AuV93LOPcE</a>
For real numbers, there’s the dictionary of real numbers (<a href="https://www.amazon.com/Dictionary-Real-Numbers-Jonathan-Borwein/dp/1461585120" rel="nofollow">https://www.amazon.com/Dictionary-Real-Numbers-Jonathan-Borw...</a>), <i>“a list of just over 100,000 eight-digit real numbers in the interval [0,1) that arise as the first eight digits of special values of familiar functions”</i><p>Its online equivalent is the inverse symbolic calculator (<a href="https://en.wikipedia.org/wiki/Inverse_Symbolic_Calculator" rel="nofollow">https://en.wikipedia.org/wiki/Inverse_Symbolic_Calculator</a>)
There's a version with fewer errors and typos here: <a href="http://neilsloane.com/doc/HIS50.pdf" rel="nofollow">http://neilsloane.com/doc/HIS50.pdf</a>
My favorite hard core nerd insult used to be "Your idea of a hot date is looking up dirty words in the unabridged dictionary," but now I'm going to use "Your idea of a hot date is looking up 69 in the Handbook of Integer Sequences."
> It was no mind-reading trick, the Catalan numbers are certainly the
most common sequence that people don’t know about<p>Guilty as charged! I learned about this sequence after looking it up in the OEIS, back when I was still a young student.
I'll take this opportunity to point out my favorite integer sequence, Recaman's Sequence:<p><a href="https://www.youtube.com/watch?v=FGC5TdIiT9U">https://www.youtube.com/watch?v=FGC5TdIiT9U</a>