You cannot find ONE such number. Either there is a loop that doesn't include 1, so you found a sequence of them. The other possibility if the sequence goes to infinity and so you found and infinite number of counter examples.

Of course that's one way of proving this wrong. But you have to start above 18 quadrillion. Because all the numbers less than that have been tried.

Has anyone tried really, really large numbers picked at random?

One approach. But I'd suggest it has less than a one-in-18-quadrillion chance of working. From the statistics so far.

It's trivial to do. Here: https://js.do/code/383036

How would you calculate the number sequence out to infinity?

I guess my question was more “what could that mean?”