HexesofVexes

Let $\mu(x)=0$ if $\exists y<x\mu(y)=0$ or $x$ is the 20 millionth prime. $\mu(x)=\mu(x+1)+1$ otherwise. The elements of the sequence only become defined once the 20 millionth prime is found; till then they’ve yet to be constructed.

Bonus: The sequence $\nu$ is defined as follows.

Let $\nu(x)=0$ if $\exists y\leq x\mu(y)$ is perfect. $\nu(x)=\nu(x+1)+1$ otherwise.

We’re not sure if this is a sequence, even though it is algorithmically definable. Its existence relies on the existence of an odd perfect number.

It’s possible to define an infinite sequence whose nth term must exist before it’s first.

Tap water anywhere near London.

It’s like drinking chalk.

Ah yes, the “delete system32 to free up space” of the modern era.

And now “Epstein Island” just became “Pedobear Paradise” in my brain. Thanks for that.

I just want to add, this is coming from someone who has completed a mathematics PhD, and so has a very very high bar for psychosis (seriously, math departments are fun, but also FUN).