The On-Line Encyclopedia of Integer Sequences [pdf]

https://oeis.org/ It's easy to accidentally spend an hour browsing sequences. One of my favorite things on the internet.

If you're ever dealing with a sequence of numbers and wondering if there's an underlying structure, this is a great place to start.

The OEIS is an incredible tool for math research. I'm happy it exists.

That first "rejected" sequence is actually pretty close to something quiet interesting.