
The On-Line Encyclopedia of Integer Sequences - gballan
https://oeis.org/
======
pdkl95
When you plot the "importance" N(n) of the positive integers, where

    
    
        N(n) = The number of occurrences of n in the OEIS
    

an interesting anomaly appears[1]. The "importance" of the integers fall into
two clusters, separated by _Sloane 's Gap_[2][3].

Also, Neil Sloane appeared[4] several times on Numberphile. In the last few
videos of that[4] playlist ("Amazing Graphs"), Sloane shares some of the
particularly interesting sequences from the OEIS.

[1] [https://i.stack.imgur.com/vcNYb.png](https://i.stack.imgur.com/vcNYb.png)

[2] [https://arxiv.org/abs/1101.4470v2](https://arxiv.org/abs/1101.4470v2)

[3]
[https://www.youtube.com/watch?v=_YysNM2JoFo](https://www.youtube.com/watch?v=_YysNM2JoFo)

[4]
[https://www.youtube.com/playlist?list=PLt5AfwLFPxWJXQqPe_llz...](https://www.youtube.com/playlist?list=PLt5AfwLFPxWJXQqPe_llzWmTHMPb9QvV2)

------
dang
Many previous threads:
[https://hn.algolia.com/?dateRange=all&page=0&prefix=true&que...](https://hn.algolia.com/?dateRange=all&page=0&prefix=true&query=The%20On-
Line%20Encyclopedia%20of%20Integer%20Sequences%20comments%3E1&sort=byDate&type=story)

(On HN, reposts are ok after a year or so:
[https://news.ycombinator.com/newsfaq.html](https://news.ycombinator.com/newsfaq.html))

------
JNRowe
An episode of Numberphile from back in August¹ had a great interview with the
creator. His enthusiasm is /still/ huge.

1\. [https://www.numberphile.com/podcast/neil-
sloane](https://www.numberphile.com/podcast/neil-sloane)

~~~
abfar
I haven't checked the podcast, but the YouTube channel has uploaded some
videos featuring him pretty recently, which I found to be very amusing.

------
ludwigvan
A fun question I have been pondering recently: what is the smallest positive
integer that has not yet been written or uttered by a human being?

~~~
braythwayt
Were Raymond Smullyan still with us, he would point out that you just answered
your own question. And yet didn't. In which case you did. Provided you didn't.

Another example:

"The smallest integer that has a description too long to fit in a Hacker News
comment."

~~~
chongli
These sorts of self-referential statements are actually forbidden in the
axioms of Zermelo-Fraenkel set theory because they require unrestricted
comprehension [1]. ZF set theory specifically restricted comprehension to
avoid Russell’s paradox [2] as well as countless other statements, like these,
which lead to absurdities in math.

Fun stuff anyway!

[1]
[https://en.wikipedia.org/wiki/Axiom_schema_of_specification#...](https://en.wikipedia.org/wiki/Axiom_schema_of_specification#Unrestricted_comprehension)

[2]
[https://en.wikipedia.org/wiki/Russell%27s_paradox](https://en.wikipedia.org/wiki/Russell%27s_paradox)

~~~
braythwayt
Absolutely!

But it is more than fun to explore them, as Smullyan points out. For example,
it leads to discussions like, “What is a description?” Which is near and dear
to my heart, as it leads to “What is a program?” and, “What is the
specification of the machine that runs the program?”

~~~
chongli
Or some of my favourites:

“What is a number? Do numbers exist?”

I’ve been having a fantastic time in my philosophy of math course this term.
It’s incredible how deep and how long these debates have been running. Cantor,
Frege, Russell, Hilbert, Heyting, Gödel, Quine, and on and on!

~~~
braythwayt
I forget which book is the source of this, but I recall Smullyan writing about
(I hope I have it roughly right) asking a child whether they could prove
something they knew about mathematics or logic, and the child replied "What is
a proof?"

Smullyan said that this was--if you took it literally--an incredibly deep
question.

------
hxhxhrra
It is hard to overestimate the importance of the OEIS in enumerative
combinatorics.

I discovered the main results of my PhD thesis essentially as follows:

1\. Find complicated construction A, hoping to prove some new results.

2\. Fail to sufficiently understand/analyze A.

3\. Write computer program to analyze characteristics of A for small n.

4\. Using OEIS, discover that apparently A is (in some sense) equivalent to
some completely different construction B, which is much simpler and well-
understood.

5\. Show desired result as well as further other results using B and
variations of it.

------
ptyshevs
There is even an old competition on Kaggle to try to predict the next integer
of the given sequence.

[https://www.kaggle.com/c/integer-sequence-
learning](https://www.kaggle.com/c/integer-sequence-learning)

------
jhncls
Just 3 weeks ago someone uploaded a video of Neil Sloane talking about his
encyclopedia. At his 80th birthday he is as vivid and enthusiastic as always.

[https://vimeo.com/365825314](https://vimeo.com/365825314)

------
xvilka
It has Maple and Mathematica code, but nothing for open source alternatives,
e.g. Octave, Julia or Python. See exampe[1].

[1]
[https://oeis.org/search?q=1%2C2%2C3%2C6%2C11%2C23%2C47%2C106...](https://oeis.org/search?q=1%2C2%2C3%2C6%2C11%2C23%2C47%2C106%2C235&language=english&go=Search)

~~~
Someone
Not “nothing”. That page has PARI code. PARI is GPL licensed
([https://pari.math.u-bordeaux.fr/](https://pari.math.u-bordeaux.fr/))

------
ColinWright
I still remember being excited when I got a sequence accepted, and even more
excited to get a _second_ sequence accepted. In each case it was something I
worked on, but had been given by someone else.

Even so, happy days ...

------
sverona
Twitter bot that tweets out random visually appealing integer sequences:
[https://twitter.com/amazing_graphs](https://twitter.com/amazing_graphs)

------
droithomme
The EIS is so valuable it should be designated a Treasure of the World
Heritage of Mankind by UNESCO.

