10 ms·

The On-Line Encyclopedia of Integer Sequences

80 points by gballan 7y ago

JNRowe 7y ago
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 7y ago
  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.
dang 7y ago
Many previous threads: https://hn.algolia.com/?dateRange=all&page=0&prefix=true&query=The%20On-Line%20Encyclopedia%20of%20Integer%20Sequences%20comments%3E1&sort=byDate&type=story https://hn.algolia.com/?dateRange=all&page=0&prefix=true&que... (On HN, reposts are ok after a year or so: https://news.ycombinator.com/newsfaq.html https://news.ycombinator.com/newsfaq.html)
ludwigvan 7y ago
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 7y ago
  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."
  - zzo38computer 7y ago
    What is the limit? This <textarea> element does not specify one, nor do I see any limit mentioned in the text of this web page.
    - saagarjha 7y ago
      I want to post an extremely long comment and see what the limit is now…
      - feikname 7y ago
        It seems to be 10k chars. Otherwise, it displays a "message too long" error.
        braythwayt 7y ago
        10k characters might be a browser limit, but I tried pasting 9,000 characters from one of my essays into a comment, and it was also rejected as being too long.
  - ivalm 7y ago
    But you can definitely say "what is the meta information or algorithm to compute X". E.g. Pi is an irrational number, but we have a bunch of ways to specify pi (we just can't explicitly write down the full sequence of numbers). Another interesting thing, while the full sequence is not computable, any particular precision IS computable (ie for any number Y that you can write down exactly, you can compute the Y'th digit of pi).
  - chongli 7y ago
    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#Unrestricted_comprehension https://en.wikipedia.org/wiki/Axiom_schema_of_specification#... [2] https://en.wikipedia.org/wiki/Russell%27s_paradox https://en.wikipedia.org/wiki/Russell%27s_paradox
- booleandilemma 7y ago
  Reminds me of this: https://en.m.wikipedia.org/wiki/Interesting_number_paradox https://en.m.wikipedia.org/wiki/Interesting_number_paradox
- missblit 7y ago
  You can try to get a rough idea by doing web searches for various random integers of different lengths (courtesy of random.org, which graced me with lots of 7's). 7 - A lucky number 92 - How old Lady Gaga wants to be when she retires 420 - A class of dinghy 7260 - A wireless card 5108 - A section in the U.S. Code about supplemental claims 51664 - A hydraulic filter 794101 - A postal code in India 7578146 - A patent number of a knitting loom clip 74703567 - A clothing trademark serial number for "authentic bad lands" 760314276 - No useful search results. 2641309883 - No useful search results 24235991397 - One (useless) search result 415865230233 - Zero search results
- nabla9 7y ago
  Every time you answer the question the correct answer changes.
  - rsrsrs86 7y ago
    Side effects in math!!!!!!!!!!
- Someone 7y ago
  If you limit it to mathematicians, it was, at some time, 8795 ;-) (https://oeis.org/wiki/Frequency_of_appearance_in_the_OEIS_database https://oeis.org/wiki/Frequency_of_appearance_in_the_OEIS_da...) More interestingly, the set of integers seems to be split into two sets: those that occur relatively often, and those that occur relatively rarely (same page)
droithomme 7y ago
The EIS is so valuable it should be designated a Treasure of the World Heritage of Mankind by UNESCO.
pdkl95 7y ago
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_llzWmTHMPb9QvV2 https://www.youtube.com/playlist?list=PLt5AfwLFPxWJXQqPe_llz...
ptyshevs 7y ago
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
ColinWright 7y ago
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 ...
xvilka 7y ago
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%2C235&language=english&go=Search https://oeis.org/search?q=1%2C2%2C3%2C6%2C11%2C23%2C47%2C106...
- Someone 7y ago
  Not “nothing”. That page has PARI code. PARI is GPL licensed (https://pari.math.u-bordeaux.fr/ https://pari.math.u-bordeaux.fr/)
jhncls 7y ago
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
hxhxhrra 7y ago
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.
sverona 7y ago
Twitter bot that tweets out random visually appealing integer sequences: https://twitter.com/amazing_graphs https://twitter.com/amazing_graphs

80 points by gballan 7y ago

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 7y ago
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.

dang 7y ago

Many previous threads: https://hn.algolia.com/?dateRange=all&page=0&prefix=true&query=The%20On-Line%20Encyclopedia%20of%20Integer%20Sequences%20comments%3E1&sort=byDate&type=story https://hn.algolia.com/?dateRange=all&page=0&prefix=true&que... (On HN, reposts are ok after a year or so: https://news.ycombinator.com/newsfaq.html https://news.ycombinator.com/newsfaq.html)

ludwigvan 7y ago

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 7y ago
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."
- zzo38computer 7y ago
  What is the limit? This <textarea> element does not specify one, nor do I see any limit mentioned in the text of this web page.
  - saagarjha 7y ago
    I want to post an extremely long comment and see what the limit is now…
    - feikname 7y ago
      It seems to be 10k chars. Otherwise, it displays a "message too long" error.
      - braythwayt 7y ago
        10k characters might be a browser limit, but I tried pasting 9,000 characters from one of my essays into a comment, and it was also rejected as being too long.
- ivalm 7y ago
  But you can definitely say "what is the meta information or algorithm to compute X". E.g. Pi is an irrational number, but we have a bunch of ways to specify pi (we just can't explicitly write down the full sequence of numbers). Another interesting thing, while the full sequence is not computable, any particular precision IS computable (ie for any number Y that you can write down exactly, you can compute the Y'th digit of pi).
- chongli 7y ago
  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#Unrestricted_comprehension https://en.wikipedia.org/wiki/Axiom_schema_of_specification#... [2] https://en.wikipedia.org/wiki/Russell%27s_paradox https://en.wikipedia.org/wiki/Russell%27s_paradox
booleandilemma 7y ago
Reminds me of this: https://en.m.wikipedia.org/wiki/Interesting_number_paradox https://en.m.wikipedia.org/wiki/Interesting_number_paradox
missblit 7y ago
You can try to get a rough idea by doing web searches for various random integers of different lengths (courtesy of random.org, which graced me with lots of 7's). 7 - A lucky number 92 - How old Lady Gaga wants to be when she retires 420 - A class of dinghy 7260 - A wireless card 5108 - A section in the U.S. Code about supplemental claims 51664 - A hydraulic filter 794101 - A postal code in India 7578146 - A patent number of a knitting loom clip 74703567 - A clothing trademark serial number for "authentic bad lands" 760314276 - No useful search results. 2641309883 - No useful search results 24235991397 - One (useless) search result 415865230233 - Zero search results
nabla9 7y ago
Every time you answer the question the correct answer changes.
- rsrsrs86 7y ago
  Side effects in math!!!!!!!!!!
Someone 7y ago
If you limit it to mathematicians, it was, at some time, 8795 ;-) (https://oeis.org/wiki/Frequency_of_appearance_in_the_OEIS_database https://oeis.org/wiki/Frequency_of_appearance_in_the_OEIS_da...) More interestingly, the set of integers seems to be split into two sets: those that occur relatively often, and those that occur relatively rarely (same page)

droithomme 7y ago

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

pdkl95 7y ago

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_llzWmTHMPb9QvV2 https://www.youtube.com/playlist?list=PLt5AfwLFPxWJXQqPe_llz...

ptyshevs 7y ago

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

ColinWright 7y ago

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 ...

xvilka 7y ago

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

Someone 7y ago
Not “nothing”. That page has PARI code. PARI is GPL licensed (https://pari.math.u-bordeaux.fr/ https://pari.math.u-bordeaux.fr/)

jhncls 7y ago

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

hxhxhrra 7y ago

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.

sverona 7y ago

Twitter bot that tweets out random visually appealing integer sequences: https://twitter.com/amazing_graphs https://twitter.com/amazing_graphs