Thread by @ccanonne_

📊 It's Thursday, time for our weekly (but weakly so) quiz! This week: integers, and remarkable sequences.

See this as an extended ad for the OEIS, if you will. Also, if you don't know the OEIS: go check it out (and come back)! oeis.org

1/

Let's start with a "fun" one. To be unhelpful, let's say as a hint that I'm expanding exp(e^x-1) as a series around 0, and am interested in the coefficients

Q1: Guess what number comes next—maybe this sequence will ring a bell? [There might be a trap]
1, 1, 2, 5, 15, 52, ??

2/

We won't do too many of those "guess what's next" games though, since they are mostly meaningless. But let's mention that, of course, @xkcdComic has a comic about integer sequences, because XKCD is basically Borges' library for the Internet.
xkcd.com/2016/
3/

Next question: a lot of integer sequences have a combinatorial or interesting raison d'être, and many are named after their "discoverer" or at least have an interesting name.
Q2: which one of those did I make up?

4/

We're going to get back to that at the end, but first, a look at prime numbers.

There are a lot of "types" of prime numbers. For instance, the set of even prime numbers is pretty small.

Q3: Which one of those sets is known to contain infinitely many prime numbers?

5/

Now, let's see. We have all those strange sequences—they are all infinite, there are too many to even consider, so let's focus on a few interesting ones.

Q4: which one of the below sequences grows the fastest?

5/

And as promised, to conclude... other funny names. There are so many of them. So. Many.

Q5: Which one of the names below did I make up?

6/

That's all for today! Of course, we didn't even scratch the surface of all the bizarre, interesting, or boring things I could have asked.

As usual, answers and discussions tomorrow. In the meantime, feel free to comment (and/or give your favourite integer sequence) below!

7/end