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Online Encyclopedia of Integer Sequences

232 点作者 hyperific大约 1 年前

21 条评论

segfaultbuserr大约 1 年前
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.<p>Thanks Neil Sloane and OEIS.
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aquafox大约 1 年前
Fun fact: The sequences of ceiling( 2 &#x2F; (2^(1&#x2F;n)-1) ) and floor( 2n &#x2F; log(2) ) have identical elements for a very long time. The first time they differ is n = 777451915729368.<p><a href="https:&#x2F;&#x2F;oeis.org&#x2F;A129935" rel="nofollow">https:&#x2F;&#x2F;oeis.org&#x2F;A129935</a>
OldGuyInTheClub大约 1 年前
Numberphile videos featuring Neil Sloane, the founder of the feast.<p><a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=RGQe8waGJ4w&amp;list=PLt5AfwLFPxWJXQqPe_llzWmTHMPb9QvV2" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=RGQe8waGJ4w&amp;list=PLt5AfwLFPx...</a>
dang大约 1 年前
Related. Others? These are just the obvious matches:<p><i>The On-Line Encyclopedia of Integer Sequences</i> - <a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=37041585">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=37041585</a> - Aug 2023 (3 comments)<p><i>What number comes next? The On-line Encyclopedia of Integer Sequences knows</i> - <a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=36038302">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=36038302</a> - May 2023 (37 comments)<p><i>The On-Line Encyclopedia of Integer Sequences</i> - <a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=26848517">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=26848517</a> - April 2021 (31 comments)<p><i>The On-Line Encyclopedia of Integer Sequences</i> - <a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=21366618">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=21366618</a> - Oct 2019 (28 comments)<p><i>The On-Line Encyclopedia of Integer Sequences [pdf]</i> - <a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=18015493">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=18015493</a> - Sept 2018 (4 comments)<p><i>The On-Line Encyclopedia of Integer Sequences</i> - <a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=15900294">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=15900294</a> - Dec 2017 (1 comment - but it says &quot;I recently had a sequence accepted&quot;)<p><i>Pictures from the On-Line Encyclopedia of Integer Sequences</i> - <a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=11711212">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=11711212</a> - May 2016 (5 comments)<p><i>The On-Line Encyclopedia of Integer Sequences</i> - <a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=9919535">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=9919535</a> - July 2015 (19 comments)<p><i>The On-Line Encyclopedia of Integer Sequences</i> - <a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=6650490">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=6650490</a> - Oct 2013 (20 comments)<p><i>The On-Line Encyclopedia of Integer Sequences</i> - <a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=2496629">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=2496629</a> - April 2011 (7 comments)<p><i>The On-Line Encyclopedia of Integer Sequences</i> - <a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=888577">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=888577</a> - Oct 2009 (2 comments)
Hnrobert42大约 1 年前
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.
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StevenXC大约 1 年前
Those interested in databases of mathematical objects may want to check out <a href="https:&#x2F;&#x2F;mathbases.org" rel="nofollow">https:&#x2F;&#x2F;mathbases.org</a>
jes5199大约 1 年前
I recently learned this was originally a book! <a href="https:&#x2F;&#x2F;www.amazon.com&#x2F;Encyclopedia-Integer-Sequences-N-Sloane&#x2F;dp&#x2F;0125586302" rel="nofollow">https:&#x2F;&#x2F;www.amazon.com&#x2F;Encyclopedia-Integer-Sequences-N-Sloa...</a><p>also, the author, Neal Sloane is a regular on the youtube channel Numberphile, which always has fun patterns to discuss
gwern大约 1 年前
OEIS is fun but the bare homepage probably isn&#x27;t too helpful. I highly recommend Sloane&#x27;s memoir about the history of OEIS: <a href="http:&#x2F;&#x2F;neilsloane.com&#x2F;doc&#x2F;HIS50.pdf" rel="nofollow">http:&#x2F;&#x2F;neilsloane.com&#x2F;doc&#x2F;HIS50.pdf</a> &quot;_A Handbook of Integer Sequences_ 50 Years Later&quot;, Sloane 2023
alganet大约 1 年前
Data can also be downloaded to use it offline <a href="https:&#x2F;&#x2F;github.com&#x2F;oeis&#x2F;oeisdata">https:&#x2F;&#x2F;github.com&#x2F;oeis&#x2F;oeisdata</a>
w-m大约 1 年前
Is there any list that&#x27;s growing slower over time than the Dedekind numbers? <a href="https:&#x2F;&#x2F;oeis.org&#x2F;A000372" rel="nofollow">https:&#x2F;&#x2F;oeis.org&#x2F;A000372</a><p>New entries in the years 1897, 1940, 1946, 1965, 1991, 2023.<p>(see also &quot;Ninth Dedekind number discovered: long-known problem in mathematics solved&quot; <a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=36491677">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=36491677</a>)
User23大约 1 年前
I find Jenny’s constant useful whenever a store wants a phone number for their loyalty program.
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nickdrozd大约 1 年前
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&#x27;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&#x27;t interesting. (Trying to come up with an OEIS-worthy sequence is difficult and edifying, and a great rainy-day activity.)<p>But even if the OEIS had no standards and included every imaginable sequence, it still wouldn&#x27;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&#x27;t enough words!
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jd3大约 1 年前
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&#x27;s president[4]<p>&gt; &quot;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.&quot;<p>&gt; &quot;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&#x27;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.&quot;<p>&gt; &quot;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.&quot;[2]<p>&gt; &quot;It&#x27;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&#x27;t have anything to do with those. The next web version (which I wrote in ~2006) was CGI invoking C with an mmap&#x27;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.&quot;<p>&gt; &quot;Note that I&#x27;m only talking about the software for the &quot;interactive&quot; 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).&quot;[5]<p>[0]: <a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=39902241">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=39902241</a><p>[1]: <a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=39903685">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=39903685</a><p>[2]: <a href="https:&#x2F;&#x2F;oeis.org&#x2F;wiki&#x2F;Welcome#OEIS:_Brief_History" rel="nofollow">https:&#x2F;&#x2F;oeis.org&#x2F;wiki&#x2F;Welcome#OEIS:_Brief_History</a><p>[3]: <a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=9920020">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=9920020</a><p>[4]: <a href="https:&#x2F;&#x2F;oeisf.org&#x2F;board&#x2F;" rel="nofollow">https:&#x2F;&#x2F;oeisf.org&#x2F;board&#x2F;</a><p>[5]: <a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=9927038">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=9927038</a><p><a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;user?id=rsc">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;user?id=rsc</a>
pugworthy大约 1 年前
This just came up in a Stand-up Maths video on a curious Minecraft boat drop bug…<p><a href="https:&#x2F;&#x2F;youtu.be&#x2F;ei58gGM9Z8k" rel="nofollow">https:&#x2F;&#x2F;youtu.be&#x2F;ei58gGM9Z8k</a>
stereoabuse大约 1 年前
All sorts of fun ones here. I like this one of a NYC subway line’s stops: <a href="https:&#x2F;&#x2F;oeis.org&#x2F;A000054" rel="nofollow">https:&#x2F;&#x2F;oeis.org&#x2F;A000054</a>
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extraduder_ire大约 1 年前
There seems to be a few python libraries out there that will spit out a subset of these sequences. I know that&#x27;s pretty much the exact opposite of how you&#x27;re supposed to use this data, but I still think it&#x27;s neat.<p>Usefully, there&#x27;s a &quot;PROG&quot; entry for many sequences on this site showing one or more ways of generating the sequence.
drsopp大约 1 年前
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 &quot;my&quot; sequences from time to time<p><a href="https:&#x2F;&#x2F;oeis.org&#x2F;search?q=jostein+trondal&amp;language=english&amp;go=Search" rel="nofollow">https:&#x2F;&#x2F;oeis.org&#x2F;search?q=jostein+trondal&amp;language=english&amp;g...</a>
bestape大约 1 年前
Out of all the professionals, Neil and company are the only community willing to publish my discoveries despite the fact I&#x27;m amateur. Looking up A297189 and learning it wasn&#x27;t known to approximate 7^(1&#x2F;2) was a thrill.
optimalsolver大约 1 年前
Is there a version of this for real value sequences?<p>Also, an interesting video on Recamán&#x27;s Sequence:<p><a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=FGC5TdIiT9U" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=FGC5TdIiT9U</a>
queuebert大约 1 年前
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.
paulpauper大约 1 年前
in theory anyone can map any sequence to an interpolating polynomial, but I think those would get rejected.<p>Also: meta-sequences: a sequence of integers that has no notable properties about them or that dosn&#x27;t comprise a sequence
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