On a slight tangent, I recently read a paper on an interesting relationship between Collatz path length and Mersenne primes.

"Our main finding to report is the fact that a path length of a Mersenne prime is approximately proportional to its index for large n, namely, D(Mn) ≈ 13.45n."

Paper is at https://arxiv.org/pdf/1104.2804.pdf . WARNING: PDF.

I'm curious, why do people on HN warn about PDFs? The worst things I can imagine happening with PDFs are (1) you don't have any software that can read it (probably like .2% of HNers?) and (2) it could potentially have some malware (but the same could be said of a website)

Before the advent of built-in PDF readers in browsers, it would often either trigger a download or launch an external program, which are kind of rude behaviors to spring on someone without notice. I still have this habit (though I'll just mention "(PDF)" in a parenthetical), and I'll certainly warn about autoplaying audio or an excessive amount of ads even if I expect a good fraction of readers to have browser configs/extensions to deal with those.

Adobe is not known for their security. PDF is also known to allow remote execution via PDF. Default reader on most systems being Adobe's reader, yeah, I'd avoid it. I know this is shifting as browsers incorporate readers, but the format is tarnished.

The mobile experience for PDFs is awful.

The mobile experience for HTML/JS/CSS is awful too.

You can de-PDF anything on the arXiv by chopping off the .pdf suffix and changing the /pdf/ to /abs/.

For example, https://arxiv.org/abs/1104.2804

Thanks! I love learning little tips like that.