“A Handbook of Integer Sequences” Fifty Years Later

by zeebeecee • 4 years ago

139 45 4 years ago

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. https://m.youtube.com/playlist?list=PLt5AfwLFPxWJXQqPe_llzWm...

jl6• 4 years ago

Seconded. He has an otherworldly curiosity.

jacquesm6• 4 years ago

The OEIS lives here:

https://oeis.org/

Super useful resource.

typical182• 4 years ago

As I understand it, written in Go.

There's a mildly humorous "How do you know" exchange where someone on HN quizzes the very person most likely to know:

https://news.ycombinator.com/item?id=9920020

jacquesm6• 4 years ago

HN has had a couple of those.

totetsu• 4 years ago

Any website that lets me see "The numbers of Mozart's piano concerti" as a graph must be doing something correctly. http://oeis.org/A064172/graph

yreg• 4 years ago

I always have a need to use this on puzzle hunts, but I don't think it ever helped.

jacquesm6• 4 years ago

Quick: 2, 8, 18, 32, ?? ?

ta123456789• 4 years ago

OEIS foundation:

http://oeisf.org/

It's nice to see they have a solid plans on how to keep the website running indefinitely.

dahart2• 4 years ago

Yes, I’m also glad to hear it’s future path is already paved. Sloane described the process and history in the paper:

“In 2009, in order to ensure the long-term future of the database, I set up a non-profit foundation, The OEIS Foundation Inc., a 501(c)(3) Public Charity, whose purpose is to own, maintain and raise funds to support The On-Line Encyclopedia of Integer Se- quences or OEIS.

On October 26, 2009, I transferred the intellectual property of The On-Line Ency- clopedia of Integer Sequences to the Foundation. A new OEIS with multiple editors was launched on November 11, 2010.

Since then it has been possible for anyone in the world to propose a new sequence or an update to an existing sequence. To do this, users must first register, and then submissions are reviewed by the editors before they become a permanent part of the OEIS. Technically the OEIS is now a “moderated wiki”.

I started writing this article on November 11, 2022, noting that this marked twelve years of successful operation of the online OEIS, and also that the database is in its 59th year of existence.”

Aardwolf• 4 years ago

The one thing I wish is they had a keyword for base-ten related sequences (rather than only "base" for any base), because base ten related sequences simply are almost always going to be way more recreational maths related than base two or base three related sequences.

Isamu• 4 years ago

A classic resource. I have my own favorite sequences. Thanks Neil for this unexpected way of connecting to previous research!

ufo• 4 years ago

It was no mind-reading trick, the Catalan numbers are certainly the most common sequence that people don’t know about

Guilty as charged! I learned about this sequence after looking it up in the OEIS, back when I was still a young student.

cscheid• 4 years ago

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.

dahart2• 4 years ago

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.

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.

Here’s the NN problem Neil was working on, and the first sequence in the database: https://oeis.org/A000435

zitterbewegung• 4 years ago

Yea neural networks were actually invented in the 40s by Warren McCulloch and Walter Pitts at University of Illinois at Chicago. They had a few isolated results until GPUs and distributed computation really kicked them into high gear and that made the change in terms to “deep learning” and now GPT-3 and other networks are hyperparamaterized neural networks with millions to billions of parameters .

visarga• 4 years ago

True, but scaling has its own problems. It was necessary to find better optimisers, activation functions, regularisers, weight sharing schemes, architectures and many other ingredients to make it work. And to prepare the large datasets, and invent the whole stack of frameworks, from CUDA to HuggingFace.

We have had 250,000 ML papers written since 2012. That's a lower bound on the number of distinct experiments necessary to find the winning tickets of today. Inventing the step-activated neuron formula was less than 1% of the way here.

ISL• 4 years ago

I was part of a research group that extensively trained small neural networks for image-processing in 2001, the high-energy physics community had been using them for many years by that time.

Furthermore, I believe that the PalmPilot's handwriting-recognition engine also had a neural-network component.

Agreed that the usage has increased radically in the last twenty years, but even before the GPU-based revolution, it felt like neural networks were already broadly known and in use across the sciences and engineering. They were just slower :).

Someone• 4 years ago

For real numbers, there’s the dictionary of real numbers (https://www.amazon.com/Dictionary-Real-Numbers-Jonathan-Borw...), “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”

Its online equivalent is the inverse symbolic calculator (https://en.wikipedia.org/wiki/Inverse_Symbolic_Calculator)

lifthrasiir• 4 years ago

Or use ries: https://mrob.com/pub/ries/index.html

peter_d_sherman7• 4 years ago

"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..."

“A Handbook of Integer Sequences” Fifty Years Later

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