When you plot the "importance" N(n) of the positive integers, where<p><pre><code> N(n) = The number of occurrences of n in the OEIS
</code></pre>
an interesting anomaly appears[1]. The "importance" of the integers fall into two clusters, separated by <i>Sloane's Gap</i>[2][3].<p>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.<p>[1] <a href="https://i.stack.imgur.com/vcNYb.png" rel="nofollow">https://i.stack.imgur.com/vcNYb.png</a><p>[2] <a href="https://arxiv.org/abs/1101.4470v2" rel="nofollow">https://arxiv.org/abs/1101.4470v2</a><p>[3] <a href="https://www.youtube.com/watch?v=_YysNM2JoFo" rel="nofollow">https://www.youtube.com/watch?v=_YysNM2JoFo</a><p>[4] <a href="https://www.youtube.com/playlist?list=PLt5AfwLFPxWJXQqPe_llzWmTHMPb9QvV2" rel="nofollow">https://www.youtube.com/playlist?list=PLt5AfwLFPxWJXQqPe_llz...</a>
Many previous threads: <a href="https://hn.algolia.com/?dateRange=all&page=0&prefix=true&query=The%20On-Line%20Encyclopedia%20of%20Integer%20Sequences%20comments%3E1&sort=byDate&type=story" rel="nofollow">https://hn.algolia.com/?dateRange=all&page=0&prefix=true&que...</a><p>(On HN, reposts are ok after a year or so: <a href="https://news.ycombinator.com/newsfaq.html" rel="nofollow">https://news.ycombinator.com/newsfaq.html</a>)
An episode of Numberphile from back in August¹ had a great interview with the creator. His enthusiasm is /still/ huge.<p>1. <a href="https://www.numberphile.com/podcast/neil-sloane" rel="nofollow">https://www.numberphile.com/podcast/neil-sloane</a>
It is hard to overestimate the importance of the OEIS in enumerative combinatorics.<p>I discovered the main results of my PhD thesis essentially as follows:<p>1. Find complicated construction A, hoping to prove some new results.<p>2. Fail to sufficiently understand/analyze A.<p>3. Write computer program to analyze characteristics of A for small n.<p>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.<p>5. Show desired result as well as further other results using B and variations of it.
There is even an old competition on Kaggle to try to predict the next integer of the given sequence.<p><a href="https://www.kaggle.com/c/integer-sequence-learning" rel="nofollow">https://www.kaggle.com/c/integer-sequence-learning</a>
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.<p><a href="https://vimeo.com/365825314" rel="nofollow">https://vimeo.com/365825314</a>
It has Maple and Mathematica code, but nothing for open source alternatives, e.g. Octave, Julia or Python. See exampe[1].<p>[1] <a href="https://oeis.org/search?q=1%2C2%2C3%2C6%2C11%2C23%2C47%2C106%2C235&language=english&go=Search" rel="nofollow">https://oeis.org/search?q=1%2C2%2C3%2C6%2C11%2C23%2C47%2C106...</a>
I still remember being excited when I got a sequence accepted, and even more excited to get a <i>second</i> sequence accepted. In each case it was something I worked on, but had been given by someone else.<p>Even so, happy days ...
Twitter bot that tweets out random visually appealing integer sequences: <a href="https://twitter.com/amazing_graphs" rel="nofollow">https://twitter.com/amazing_graphs</a>