The OEIS lives here: https://oeis.org/ Super useful resource.
OEIS foundation:
It's nice to see they have a solid plans on how to keep the website running indefinitely.
“A Handbook of Integer Sequences” Fifty Years Later
11–20 of 46 posts
Re: “A Handbook of Integer Sequences” Fifty Years Later
#12> 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
Re: “A Handbook of Integer Sequences” Fifty Years Later
#13Neil 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...
Seconded. He has an otherworldly curiosity.
Re: “A Handbook of Integer Sequences” Fifty Years Later
#14The OEIS lives here: https://oeis.org/ Super useful resource.
OEIS foundation: http://oeisf.org/ It's nice to see they have a solid plans on how to keep the website running indefinitely.
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.”
Re: “A Handbook of Integer Sequences” Fifty Years Later
#15For 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)
Re: “A Handbook of Integer Sequences” Fifty Years Later
#16>"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..."
Related Mathologer video:
Mathologer - "Why don't they teach Newton's calculus of 'What comes next?'"
Re: “A Handbook of Integer Sequences” Fifty Years Later
#17For 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 )
Or use ries: https://mrob.com/pub/ries/index.html
Re: “A Handbook of Integer Sequences” Fifty Years Later
#18>"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..." Related Mathologer video: Mathologer - "Why don't they teach Newton's calculus of 'What comes next?…
The finite difference method of that video is only useful for finding polynomial sequences. Of course, any finite sequence can be extended to some polynomial, but in many cases (such as this one) that’s not the result you’re looking for.
Re: “A Handbook of Integer Sequences” Fifty Years Later
#19Re: “A Handbook of Integer Sequences” Fifty Years Later
#20My 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."