Also "Why is <number> interesting?" is an interesting question to ask. It finds something interesting about most integers, and falls back to giving you a good rational approximation for 'uninteresting' reals.
> It finds something interesting about most integers
Every integer is interesting. "[...] if there exists a non-empty set of uninteresting natural numbers, there would be a smallest uninteresting number – but the smallest uninteresting number is itself interesting because it is the smallest uninteresting number [...]" (https://en.wikipedia.org/wiki/Interesting_number_paradox)
A few days ago, I got to thinking about this. On a theoretical level every integer is interesting due to that, but on a practical level there's not much point calling a number "interesting" if the only property giving it that quality is being the first uninteresting number larger than n-1.
One way of checking what makes a number interesting is seeing what sequences it is in in the OEIS[1]. Interesting properties (squares, primes, palindromes, friendly numbers, etc) all have the first hundred or so numbers with those properties in a list. So I downloaded the dataset of all sequences from OEIS, and iterated through all integers to find the first one that is not in any sequence in the OEIS.
So, I present the smallest uninteresting number: 20,067. Every number before it is in at least one of the sequences - for example, 20,066 is 'a partial sum for a coordination sequence for the "pcu-i" 3D uniform tiling'. It is the first number that has no interesting properties other than trivial ones (like being a multiple of 3). It is the first uninteresting number, but one could say that makes it meta-interesting rather than being interesting in and of itself.
Edit: and after doing all that work I saw that someone else has already done so and put it in the wikipedia article. Oh well, at least I learned about set processing in Python.
