12 ms·

Online Encyclopedia of Integer Sequences

232 points by hyperific 3y ago

Hnrobert42 3y ago
Oh man. I love this encylopedia. Once, I found a little website that had a series of increasingly difficult, Project Euler style coding problems. After a while, it turned out to be a google recruiting tool. But while I was playing the games, I had to use the OEIS more than once. It’s such an obscure, nerdy tool. I realky like it.
- kccqzy 3y ago
  The website you mention was, I believe, Google Foobar. Here's a nice article about it https://www.turing.com/kb/foobar-google-secret-hiring-technique https://www.turing.com/kb/foobar-google-secret-hiring-techni... It was internally called Rabbit Hole. In true killed-by-Google fashion, they killed this recruiting tool too. It was formerly available at https://foobar.withgoogle.com/ https://foobar.withgoogle.com/ They also used to have on-site versions of such programming contests. I've been to the one at their Los Angeles office twice. Very nice memories.
  - fsmv 3y ago
    It still exists. I saw it pop up when I searched about LSTMs a few weeks ago.
    - PurelyApplied 3y ago
      It was turned down three days ago.
- ok123456 3y ago
  I did the same thing. I solved all the levels. I got random emails from Google trying to recruit me for a while. I had no interest in working for them. I just wanted to solve programming puzzles in a time before it got dysfunctionally commodified industry-wide.
stereoabuse 3y ago
All sorts of fun ones here. I like this one of a NYC subway line’s stops: https://oeis.org/A000054 https://oeis.org/A000054
- ssalka 3y ago
  I was delighted to find The Numbers from LOST: https://oeis.org/A104101 https://oeis.org/A104101
  - twic 3y ago
    > It is easy to fit formulas to the first six terms, in a million different ways, but none of them are of any interest (the seventh term can be chosen to be any number you wish). - N. J. A. Sloane, Oct 22 2017 A microcosm for the "plot" of that show, where the writers just pulled some new twist out of their backsides every episode!
paulpauper 3y ago
in theory anyone can map any sequence to an interpolating polynomial, but I think those would get rejected. Also: meta-sequences: a sequence of integers that has no notable properties about them or that dosn't comprise a sequence
- StevenXC 3y ago
  I like the phrasing used by https://houseofgraphs.org/ https://houseofgraphs.org/ — while there are an infinite number of mathematical objects in any category, there are only "a few thousand that can be considered really interesting."
  - nurettin 3y ago
    The same with chess and go. There are way too many move order combinations, but only a few thousand interesting ones.
    - tromp 3y ago
      Happy to have authored A094777, Number of legal positions in Go played on an n X n grid (each group must have at least one liberty), [1] and A269417, Number of Go games on n X n board with no repeating position and suicide allowed. [2]. [1] https://oeis.org/A094777 https://oeis.org/A094777 [2] https://oeis.org/A269417 https://oeis.org/A269417
- MatthiasPortzel 3y ago
  Relevant XKCD: https://xkcd.com/2016/ https://xkcd.com/2016/
  - omoikane 3y ago
    I can't find any sequences that list Randall Munroe as the author, but there are several sequences that referenced xkcd: https://oeis.org/search?q=xkcd&go=Search https://oeis.org/search?q=xkcd&go=Search https://oeis.org/search?q=randall+munroe&go=Search https://oeis.org/search?q=randall+munroe&go=Search
StevenXC 3y ago
Those interested in databases of mathematical objects may want to check out https://mathbases.org https://mathbases.org
OldGuyInTheClub 3y ago
Numberphile videos featuring Neil Sloane, the founder of the feast. https://www.youtube.com/watch?v=RGQe8waGJ4w&list=PLt5AfwLFPxWJXQqPe_llzWmTHMPb9QvV2 https://www.youtube.com/watch?v=RGQe8waGJ4w&list=PLt5AfwLFPx...
dang 3y ago
Related. Others? These are just the obvious matches: The On-Line Encyclopedia of Integer Sequences - https://news.ycombinator.com/item?id=37041585 https://news.ycombinator.com/item?id=37041585 - Aug 2023 (3 comments) What number comes next? The On-line Encyclopedia of Integer Sequences knows - https://news.ycombinator.com/item?id=36038302 https://news.ycombinator.com/item?id=36038302 - May 2023 (37 comments) The On-Line Encyclopedia of Integer Sequences - https://news.ycombinator.com/item?id=26848517 https://news.ycombinator.com/item?id=26848517 - April 2021 (31 comments) The On-Line Encyclopedia of Integer Sequences - https://news.ycombinator.com/item?id=21366618 https://news.ycombinator.com/item?id=21366618 - Oct 2019 (28 comments) The On-Line Encyclopedia of Integer Sequences [pdf] - https://news.ycombinator.com/item?id=18015493 https://news.ycombinator.com/item?id=18015493 - Sept 2018 (4 comments) The On-Line Encyclopedia of Integer Sequences - https://news.ycombinator.com/item?id=15900294 https://news.ycombinator.com/item?id=15900294 - Dec 2017 (1 comment - but it says "I recently had a sequence accepted") Pictures from the On-Line Encyclopedia of Integer Sequences - https://news.ycombinator.com/item?id=11711212 https://news.ycombinator.com/item?id=11711212 - May 2016 (5 comments) The On-Line Encyclopedia of Integer Sequences - https://news.ycombinator.com/item?id=9919535 https://news.ycombinator.com/item?id=9919535 - July 2015 (19 comments) The On-Line Encyclopedia of Integer Sequences - https://news.ycombinator.com/item?id=6650490 https://news.ycombinator.com/item?id=6650490 - Oct 2013 (20 comments) The On-Line Encyclopedia of Integer Sequences - https://news.ycombinator.com/item?id=2496629 https://news.ycombinator.com/item?id=2496629 - April 2011 (7 comments) The On-Line Encyclopedia of Integer Sequences - https://news.ycombinator.com/item?id=888577 https://news.ycombinator.com/item?id=888577 - Oct 2009 (2 comments)
User23 3y ago
I find Jenny’s constant useful whenever a store wants a phone number for their loyalty program.
- anArbitraryOne 3y ago
  Did they ever find the area code for that, or is that still unsolved?
- generationP 3y ago
  I think Lenny's constant might be better suited https://old.reddit.com/r/itslenny/ https://old.reddit.com/r/itslenny/
segfaultbuserr 3y ago
OEIS solves real-world problems! One time I needed to optimize accesses to a data structure in my code. By trying out a few examples, I found the optimal order of iterations followed a particular number sequence, but I had no idea on how it could be deduced or calculated analytically. I entered the few examples I had into OEIS and found the solution. The solution involves graduate-level combinatorics and there was no way that I could solve it. Thanks Neil Sloane and OEIS.
- JoshTriplett 3y ago
  This sounds fascinating! What was the structure, and what was the sequence?
  - segfaultbuserr 3y ago
    I can't give any detail, but the solution to my problem involves k-variate k-nomial multinomial coefficients [1]. It's a generalization of the binomial coefficients to high-order scenarios such as trinomial coefficients, quadrinomial coefficients, etc. In other words, from a Pascal triangle to a Pascal pyramid, to a Pascal hyperpyramid. [1] https://oeis.org/wiki/Multinomial_coefficients https://oeis.org/wiki/Multinomial_coefficients
    - Tainnor 3y ago
      Multinomial coefficients are also used to define the multinomial distribution in probability which models e.g. the problem of "if I throw a fair die n times, how likely is it that I get exactly x1 ones, x2 twos, ..., x6 sixes?" - which is a generalisation of the binomial distribution in which there are only two cases.
    - bdjsiqoocwk 3y ago
      This is not "graduate-level", it's a straightforward generalization of something that all school age kids learn. (Which is not too say that it's trivial to obtain an expression. I'm just saying it's not conceptually advanced)
jd3 3y ago
Russ Cox (who recently did a deep dive into the xz attack shell script[0][1]) of Bell Labs Plan9 and Google golang fame re-wrote the OEIS in golang in the summer of 2009[2][3] and now serves as the foundation's president[4] > "Here, however, we ran into a very serious problem. In the summer of 2009, when we tried to get the OEIS working as a wiki, we discovered that the Mediawiki software was not capable of handling the kind of queries that arise in looking up sequences. This was a disaster." > "It took us over a year to resolve this problem. In the end, Russ Cox completely rewrote all the programs needed to maintain the database and answer queries - a huge task! NJAS's colleague David Applegate has also been of enormous help in getting the new system working. As a result of their work, the new OEIS was finally launched on November 11, 2010. It is now 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. A group of about 130 editors has been formed, whose job it is to review submissions before they become a permanent part of the OEIS." > "So, after nearly two years of struggle, the OEIS was finally able to operate without NJAS having to approve every change. After 46 years of running the database, this came as a great relief to him."[2] > "It's true. The original software was an email auto-reply implemented in shell. The first web version of the software was CGI invoking roughly the same shell script. I didn't have anything to do with those. The next web version (which I wrote in ~2006) was CGI invoking C with an mmap'ed index file. The third web version (which I wrote in ~2010 and is the one running today) is a Go HTTP server, fronted by Apache." > "Note that I'm only talking about the software for the "interactive" UI, not the database itself. The database itself goes back to punched cards and the original interactive UI was a pair of published books (first A Handbook of Integer Sequences, and then the Encyclopedia of Integer Sequences)."[5] [0]: https://news.ycombinator.com/item?id=39902241 https://news.ycombinator.com/item?id=39902241 [1]: https://news.ycombinator.com/item?id=39903685 https://news.ycombinator.com/item?id=39903685 [2]: https://oeis.org/wiki/Welcome#OEIS:_Brief_History https://oeis.org/wiki/Welcome#OEIS:_Brief_History [3]: https://news.ycombinator.com/item?id=9920020 https://news.ycombinator.com/item?id=9920020 [4]: https://oeisf.org/board/ https://oeisf.org/board/ [5]: https://news.ycombinator.com/item?id=9927038 https://news.ycombinator.com/item?id=9927038 https://news.ycombinator.com/user?id=rsc https://news.ycombinator.com/user?id=rsc
drsopp 3y ago
I love this site. I have used it many times to help me solve- or shine a light on some problems I have worked on. I visit "my" sequences from time to time https://oeis.org/search?q=jostein+trondal&language=english&go=Search https://oeis.org/search?q=jostein+trondal&language=english&g...
optimalsolver 3y ago
Is there a version of this for real value sequences? Also, an interesting video on Recamán's Sequence: https://www.youtube.com/watch?v=FGC5TdIiT9U https://www.youtube.com/watch?v=FGC5TdIiT9U
aquafox 3y ago
Fun fact: The sequences of ceiling( 2 / (2^(1/n)-1) ) and floor( 2n / log(2) ) have identical elements for a very long time. The first time they differ is n = 777451915729368. https://oeis.org/A129935 https://oeis.org/A129935
alganet 3y ago
Data can also be downloaded to use it offline https://github.com/oeis/oeisdata https://github.com/oeis/oeisdata
w-m 3y ago
Is there any list that's growing slower over time than the Dedekind numbers? https://oeis.org/A000372 https://oeis.org/A000372 New entries in the years 1897, 1940, 1946, 1965, 1991, 2023. (see also "Ninth Dedekind number discovered: long-known problem in mathematics solved" https://news.ycombinator.com/item?id=36491677 https://news.ycombinator.com/item?id=36491677)
nickdrozd 3y ago
The OEIS is a curated selection of integer sequences. It only includes those sequences deemed interesting (usually mathematically, but also recreationally, and occasionally for some other reason). It's easy to generate a new sequence from an old one, say B(n) = A(n) + 11 for some sequence A. But if you submit that it will be rejected because it isn't interesting. (Trying to come up with an OEIS-worthy sequence is difficult and edifying, and a great rainy-day activity.) But even if the OEIS had no standards and included every imaginable sequence, it still wouldn't include more than a vanishingly small fraction of the total set of all integer sequences. This is because almost all integer sequences are infinitely long and cannot be specified. There just aren't enough words!
- tkw01536 3y ago
  At one point a project in a research group I'm part of did automatic parsing of the entire OEIS to find relations between different existing sequences. Using a very simple approach, they found ~300 000 000 relations (e.g. meaning one sequence can be expressed as some combination of other sequences); see section 4 of [1]. However they submitted only three (!) of those back to OEIS. Even with 130 reviewers on the OEIS side, submitting all of those relations would have basically been a Denial-of-service attack on the review process. [1] https://kwarc.info/people/mkohlhase/papers/icms16-oeis.pdf https://kwarc.info/people/mkohlhase/papers/icms16-oeis.pdf
- sa46 3y ago
  Is the set of integer sequences uncountably infinite? It seems like Cantor's diagonal argument would work here. 1. Number all sets from 0. 2. Construct a new set by picking the i^th number from each set.
  - nickdrozd 3y ago
    Yes, one useful application of Cantor's theorem is to show that anything claiming to enumerate all integer sequences must fail to do so. That's assuming that the sequences can be infinite; if it were the Online Encyclopedia of Finite Integer Sequences, then it could succeed at enumerating all of them. (As for the diagonal argument, make sure that the ith value of the counter-sequence DIFFERS from the ith value of the ith sequence. A sequence whose ith value matches the ith value of the ith sequence doesn't produce a contradiction, and could in fact be part of the encyclopedia.)
pugworthy 3y ago
This just came up in a Stand-up Maths video on a curious Minecraft boat drop bug… https://youtu.be/ei58gGM9Z8k https://youtu.be/ei58gGM9Z8k
queuebert 3y ago
Using the OEIS, you can usually find a reason why every single answer to those IQ questions about what number comes next in the series is correct.
jes5199 3y ago
I recently learned this was originally a book! https://www.amazon.com/Encyclopedia-Integer-Sequences-N-Sloane/dp/0125586302 https://www.amazon.com/Encyclopedia-Integer-Sequences-N-Sloa... also, the author, Neal Sloane is a regular on the youtube channel Numberphile, which always has fun patterns to discuss
gwern 3y ago
OEIS is fun but the bare homepage probably isn't too helpful. I highly recommend Sloane's memoir about the history of OEIS: http://neilsloane.com/doc/HIS50.pdf http://neilsloane.com/doc/HIS50.pdf "_A Handbook of Integer Sequences_ 50 Years Later", Sloane 2023
extraduder_ire 3y ago
There seems to be a few python libraries out there that will spit out a subset of these sequences. I know that's pretty much the exact opposite of how you're supposed to use this data, but I still think it's neat. Usefully, there's a "PROG" entry for many sequences on this site showing one or more ways of generating the sequence.
bestape 2y ago
Out of all the professionals, Neil and company are the only community willing to publish my discoveries despite the fact I'm amateur. Looking up A297189 and learning it wasn't known to approximate 7^(1/2) was a thrill.

232 points by hyperific 3y ago

Oh man. I love this encylopedia. Once, I found a little website that had a series of increasingly difficult, Project Euler style coding problems. After a while, it turned out to be a google recruiting tool. But while I was playing the games, I had to use the OEIS more than once. It’s such an obscure, nerdy tool. I realky like it.

kccqzy 3y ago
The website you mention was, I believe, Google Foobar. Here's a nice article about it https://www.turing.com/kb/foobar-google-secret-hiring-technique https://www.turing.com/kb/foobar-google-secret-hiring-techni... It was internally called Rabbit Hole. In true killed-by-Google fashion, they killed this recruiting tool too. It was formerly available at https://foobar.withgoogle.com/ https://foobar.withgoogle.com/ They also used to have on-site versions of such programming contests. I've been to the one at their Los Angeles office twice. Very nice memories.
- fsmv 3y ago
  It still exists. I saw it pop up when I searched about LSTMs a few weeks ago.
  - PurelyApplied 3y ago
    It was turned down three days ago.
ok123456 3y ago
I did the same thing. I solved all the levels. I got random emails from Google trying to recruit me for a while. I had no interest in working for them. I just wanted to solve programming puzzles in a time before it got dysfunctionally commodified industry-wide.

stereoabuse 3y ago

All sorts of fun ones here. I like this one of a NYC subway line’s stops: https://oeis.org/A000054 https://oeis.org/A000054

ssalka 3y ago
I was delighted to find The Numbers from LOST: https://oeis.org/A104101 https://oeis.org/A104101
- twic 3y ago
  > It is easy to fit formulas to the first six terms, in a million different ways, but none of them are of any interest (the seventh term can be chosen to be any number you wish). - N. J. A. Sloane, Oct 22 2017 A microcosm for the "plot" of that show, where the writers just pulled some new twist out of their backsides every episode!

paulpauper 3y ago

in theory anyone can map any sequence to an interpolating polynomial, but I think those would get rejected. Also: meta-sequences: a sequence of integers that has no notable properties about them or that dosn't comprise a sequence

StevenXC 3y ago
I like the phrasing used by https://houseofgraphs.org/ https://houseofgraphs.org/ — while there are an infinite number of mathematical objects in any category, there are only "a few thousand that can be considered really interesting."
- nurettin 3y ago
  The same with chess and go. There are way too many move order combinations, but only a few thousand interesting ones.
  - tromp 3y ago
    Happy to have authored A094777, Number of legal positions in Go played on an n X n grid (each group must have at least one liberty), [1] and A269417, Number of Go games on n X n board with no repeating position and suicide allowed. [2]. [1] https://oeis.org/A094777 https://oeis.org/A094777 [2] https://oeis.org/A269417 https://oeis.org/A269417
MatthiasPortzel 3y ago
Relevant XKCD: https://xkcd.com/2016/ https://xkcd.com/2016/
- omoikane 3y ago
  I can't find any sequences that list Randall Munroe as the author, but there are several sequences that referenced xkcd: https://oeis.org/search?q=xkcd&go=Search https://oeis.org/search?q=xkcd&go=Search https://oeis.org/search?q=randall+munroe&go=Search https://oeis.org/search?q=randall+munroe&go=Search

StevenXC 3y ago

Those interested in databases of mathematical objects may want to check out https://mathbases.org https://mathbases.org

OldGuyInTheClub 3y ago

Numberphile videos featuring Neil Sloane, the founder of the feast. https://www.youtube.com/watch?v=RGQe8waGJ4w&list=PLt5AfwLFPxWJXQqPe_llzWmTHMPb9QvV2 https://www.youtube.com/watch?v=RGQe8waGJ4w&list=PLt5AfwLFPx...

dang 3y ago

Related. Others? These are just the obvious matches: The On-Line Encyclopedia of Integer Sequences - https://news.ycombinator.com/item?id=37041585 https://news.ycombinator.com/item?id=37041585 - Aug 2023 (3 comments) What number comes next? The On-line Encyclopedia of Integer Sequences knows - https://news.ycombinator.com/item?id=36038302 https://news.ycombinator.com/item?id=36038302 - May 2023 (37 comments) The On-Line Encyclopedia of Integer Sequences - https://news.ycombinator.com/item?id=26848517 https://news.ycombinator.com/item?id=26848517 - April 2021 (31 comments) The On-Line Encyclopedia of Integer Sequences - https://news.ycombinator.com/item?id=21366618 https://news.ycombinator.com/item?id=21366618 - Oct 2019 (28 comments) The On-Line Encyclopedia of Integer Sequences [pdf] - https://news.ycombinator.com/item?id=18015493 https://news.ycombinator.com/item?id=18015493 - Sept 2018 (4 comments) The On-Line Encyclopedia of Integer Sequences - https://news.ycombinator.com/item?id=15900294 https://news.ycombinator.com/item?id=15900294 - Dec 2017 (1 comment - but it says "I recently had a sequence accepted") Pictures from the On-Line Encyclopedia of Integer Sequences - https://news.ycombinator.com/item?id=11711212 https://news.ycombinator.com/item?id=11711212 - May 2016 (5 comments) The On-Line Encyclopedia of Integer Sequences - https://news.ycombinator.com/item?id=9919535 https://news.ycombinator.com/item?id=9919535 - July 2015 (19 comments) The On-Line Encyclopedia of Integer Sequences - https://news.ycombinator.com/item?id=6650490 https://news.ycombinator.com/item?id=6650490 - Oct 2013 (20 comments) The On-Line Encyclopedia of Integer Sequences - https://news.ycombinator.com/item?id=2496629 https://news.ycombinator.com/item?id=2496629 - April 2011 (7 comments) The On-Line Encyclopedia of Integer Sequences - https://news.ycombinator.com/item?id=888577 https://news.ycombinator.com/item?id=888577 - Oct 2009 (2 comments)

User23 3y ago

I find Jenny’s constant useful whenever a store wants a phone number for their loyalty program.

anArbitraryOne 3y ago
Did they ever find the area code for that, or is that still unsolved?
generationP 3y ago
I think Lenny's constant might be better suited https://old.reddit.com/r/itslenny/ https://old.reddit.com/r/itslenny/

segfaultbuserr 3y ago

OEIS solves real-world problems! One time I needed to optimize accesses to a data structure in my code. By trying out a few examples, I found the optimal order of iterations followed a particular number sequence, but I had no idea on how it could be deduced or calculated analytically. I entered the few examples I had into OEIS and found the solution. The solution involves graduate-level combinatorics and there was no way that I could solve it. Thanks Neil Sloane and OEIS.

JoshTriplett 3y ago
This sounds fascinating! What was the structure, and what was the sequence?
- segfaultbuserr 3y ago
  I can't give any detail, but the solution to my problem involves k-variate k-nomial multinomial coefficients [1]. It's a generalization of the binomial coefficients to high-order scenarios such as trinomial coefficients, quadrinomial coefficients, etc. In other words, from a Pascal triangle to a Pascal pyramid, to a Pascal hyperpyramid. [1] https://oeis.org/wiki/Multinomial_coefficients https://oeis.org/wiki/Multinomial_coefficients
  - Tainnor 3y ago
    Multinomial coefficients are also used to define the multinomial distribution in probability which models e.g. the problem of "if I throw a fair die n times, how likely is it that I get exactly x1 ones, x2 twos, ..., x6 sixes?" - which is a generalisation of the binomial distribution in which there are only two cases.
  - bdjsiqoocwk 3y ago
    This is not "graduate-level", it's a straightforward generalization of something that all school age kids learn. (Which is not too say that it's trivial to obtain an expression. I'm just saying it's not conceptually advanced)

jd3 3y ago

Russ Cox (who recently did a deep dive into the xz attack shell script[0][1]) of Bell Labs Plan9 and Google golang fame re-wrote the OEIS in golang in the summer of 2009[2][3] and now serves as the foundation's president[4] > "Here, however, we ran into a very serious problem. In the summer of 2009, when we tried to get the OEIS working as a wiki, we discovered that the Mediawiki software was not capable of handling the kind of queries that arise in looking up sequences. This was a disaster." > "It took us over a year to resolve this problem. In the end, Russ Cox completely rewrote all the programs needed to maintain the database and answer queries - a huge task! NJAS's colleague David Applegate has also been of enormous help in getting the new system working. As a result of their work, the new OEIS was finally launched on November 11, 2010. It is now 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. A group of about 130 editors has been formed, whose job it is to review submissions before they become a permanent part of the OEIS." > "So, after nearly two years of struggle, the OEIS was finally able to operate without NJAS having to approve every change. After 46 years of running the database, this came as a great relief to him."[2] > "It's true. The original software was an email auto-reply implemented in shell. The first web version of the software was CGI invoking roughly the same shell script. I didn't have anything to do with those. The next web version (which I wrote in ~2006) was CGI invoking C with an mmap'ed index file. The third web version (which I wrote in ~2010 and is the one running today) is a Go HTTP server, fronted by Apache." > "Note that I'm only talking about the software for the "interactive" UI, not the database itself. The database itself goes back to punched cards and the original interactive UI was a pair of published books (first A Handbook of Integer Sequences, and then the Encyclopedia of Integer Sequences)."[5] [0]: https://news.ycombinator.com/item?id=39902241 https://news.ycombinator.com/item?id=39902241 [1]: https://news.ycombinator.com/item?id=39903685 https://news.ycombinator.com/item?id=39903685 [2]: https://oeis.org/wiki/Welcome#OEIS:_Brief_History https://oeis.org/wiki/Welcome#OEIS:_Brief_History [3]: https://news.ycombinator.com/item?id=9920020 https://news.ycombinator.com/item?id=9920020 [4]: https://oeisf.org/board/ https://oeisf.org/board/ [5]: https://news.ycombinator.com/item?id=9927038 https://news.ycombinator.com/item?id=9927038 https://news.ycombinator.com/user?id=rsc https://news.ycombinator.com/user?id=rsc

drsopp 3y ago

I love this site. I have used it many times to help me solve- or shine a light on some problems I have worked on. I visit "my" sequences from time to time https://oeis.org/search?q=jostein+trondal&language=english&go=Search https://oeis.org/search?q=jostein+trondal&language=english&g...

optimalsolver 3y ago

Is there a version of this for real value sequences? Also, an interesting video on Recamán's Sequence: https://www.youtube.com/watch?v=FGC5TdIiT9U https://www.youtube.com/watch?v=FGC5TdIiT9U

aquafox 3y ago

Fun fact: The sequences of ceiling( 2 / (2^(1/n)-1) ) and floor( 2n / log(2) ) have identical elements for a very long time. The first time they differ is n = 777451915729368. https://oeis.org/A129935 https://oeis.org/A129935

alganet 3y ago

Data can also be downloaded to use it offline https://github.com/oeis/oeisdata https://github.com/oeis/oeisdata

w-m 3y ago

Is there any list that's growing slower over time than the Dedekind numbers? https://oeis.org/A000372 https://oeis.org/A000372 New entries in the years 1897, 1940, 1946, 1965, 1991, 2023. (see also "Ninth Dedekind number discovered: long-known problem in mathematics solved" https://news.ycombinator.com/item?id=36491677 https://news.ycombinator.com/item?id=36491677)

nickdrozd 3y ago

The OEIS is a curated selection of integer sequences. It only includes those sequences deemed interesting (usually mathematically, but also recreationally, and occasionally for some other reason). It's easy to generate a new sequence from an old one, say B(n) = A(n) + 11 for some sequence A. But if you submit that it will be rejected because it isn't interesting. (Trying to come up with an OEIS-worthy sequence is difficult and edifying, and a great rainy-day activity.) But even if the OEIS had no standards and included every imaginable sequence, it still wouldn't include more than a vanishingly small fraction of the total set of all integer sequences. This is because almost all integer sequences are infinitely long and cannot be specified. There just aren't enough words!

tkw01536 3y ago
At one point a project in a research group I'm part of did automatic parsing of the entire OEIS to find relations between different existing sequences. Using a very simple approach, they found ~300 000 000 relations (e.g. meaning one sequence can be expressed as some combination of other sequences); see section 4 of [1]. However they submitted only three (!) of those back to OEIS. Even with 130 reviewers on the OEIS side, submitting all of those relations would have basically been a Denial-of-service attack on the review process. [1] https://kwarc.info/people/mkohlhase/papers/icms16-oeis.pdf https://kwarc.info/people/mkohlhase/papers/icms16-oeis.pdf
sa46 3y ago
Is the set of integer sequences uncountably infinite? It seems like Cantor's diagonal argument would work here. 1. Number all sets from 0. 2. Construct a new set by picking the i^th number from each set.
- nickdrozd 3y ago
  Yes, one useful application of Cantor's theorem is to show that anything claiming to enumerate all integer sequences must fail to do so. That's assuming that the sequences can be infinite; if it were the Online Encyclopedia of Finite Integer Sequences, then it could succeed at enumerating all of them. (As for the diagonal argument, make sure that the ith value of the counter-sequence DIFFERS from the ith value of the ith sequence. A sequence whose ith value matches the ith value of the ith sequence doesn't produce a contradiction, and could in fact be part of the encyclopedia.)

pugworthy 3y ago

This just came up in a Stand-up Maths video on a curious Minecraft boat drop bug… https://youtu.be/ei58gGM9Z8k https://youtu.be/ei58gGM9Z8k

queuebert 3y ago

Using the OEIS, you can usually find a reason why every single answer to those IQ questions about what number comes next in the series is correct.

jes5199 3y ago

I recently learned this was originally a book! https://www.amazon.com/Encyclopedia-Integer-Sequences-N-Sloane/dp/0125586302 https://www.amazon.com/Encyclopedia-Integer-Sequences-N-Sloa... also, the author, Neal Sloane is a regular on the youtube channel Numberphile, which always has fun patterns to discuss

gwern 3y ago

OEIS is fun but the bare homepage probably isn't too helpful. I highly recommend Sloane's memoir about the history of OEIS: http://neilsloane.com/doc/HIS50.pdf http://neilsloane.com/doc/HIS50.pdf "_A Handbook of Integer Sequences_ 50 Years Later", Sloane 2023

extraduder_ire 3y ago

There seems to be a few python libraries out there that will spit out a subset of these sequences. I know that's pretty much the exact opposite of how you're supposed to use this data, but I still think it's neat. Usefully, there's a "PROG" entry for many sequences on this site showing one or more ways of generating the sequence.

bestape 2y ago

Out of all the professionals, Neil and company are the only community willing to publish my discoveries despite the fact I'm amateur. Looking up A297189 and learning it wasn't known to approximate 7^(1/2) was a thrill.