I had the honor of having lunch with Dr. Sloane once. By the end, the paper tablecloth was COVERED in sequences scrawled in pen. He was grinning and telling everyone at the table about different properties and new sequences being worked on.
OEIS was awesome before that, but seeing how much he really, really loves sequences made it even better. You can feel the love between every comma.
If you make a plot of how many different sequences a particular number appears in in this database, a rather interesting pattern emerges.
Some numbers appear frequently, as you would expect (primes, numbers 1 off from prime, etc) while others appear infrequently, but in general there is a downward trend as the numbers become larger. That is all expected; what isn't expected is that there seems to be a break between common numbers and uncommon numbers. A very distinct break. The theory is that social prejudices towards certain bases and certain numbers have caused mathematicians to find more sequences with numbers that they "like" than those that they don't. So for example, numbers that look neat in base 10, say "3333" or "4444" get special treatment and tend to occur in more sequences.
The paper on this weird distribution is rather accessible, I recommend it: http://arxiv.org/abs/1101.4470 Page 4 has the pretty plot.
Aye, the Numberphile video is fantastic; that's actually where I first found out about this. :) All their videos tend to be great; they're done by the same film-maker that does the "Periodic Videos" youtube channel, Brady Haran.
It's weird because this awesome site (well worth checking out) has been submitted about 10 times here and never got any comments except for this time: https://news.ycombinator.com/item?id=2496629 .. it's like there's not much to say about integer sequences or something ;-)
I spent hours on the OEIS having fun. I like to convert numerical sequencies to sound to see how they sound. Some sound bad but some sound pretty good. I wrote a little bit about this here:
Today I listened to the album The Rise and Fall of Ziggy Stardust for the first time. It was released in 1972. Is it really that bewildering to you that not everyone has seen everything that exists already?
I really enjoyed it. It's an odd experience, listening to an album that old and that well known for the first time, because almost inevitably you will have heard some of the songs before without realising where they were from. A couple of times I recognized intros or riffs but couldn't quite place them - probably from movies, advertisements, or just hearing them on the radio.
You also have to try and shed yourself of the intervening 40 years of musical and social development, to try and get a sense of why this album created such a buzz when it was released for the first time (context - I'm about 30 years old, so I wasn't even born until 10 years after this was released, and wasn't socially/musically aware until about 25 years after it came out.)
I rather like XKCDs "Lucky Ten Thousand" on this subject.
The idea is that simply because of birth rate for everything "everyone knows" there are an average 10,000 people per day are discovering it for the first time.
I was a little surprised to see this getting traction on HN too. It would be like seeing a link to the Wayback Machine or Wolfram Alpha with no qualification.
OEIS was awesome before that, but seeing how much he really, really loves sequences made it even better. You can feel the love between every comma.