@robinhouston thanks for the suggestion. The mailing list archives seem to be down, but I tried sending a subscription request to the Google group.

Meanwhile, I extended my search program and confirmed the conjecture holds up to 2^4096−1. Beyond that it's difficult to go at all, because I'm not sure how I'd test something has order exactly 2^8192−1 without knowing the prime factors of 2^8192−1 and therefore of 2^4096+1, and as far as I'm aware, nobody knows those! So I think I've collected all the data I reasonably can.

@simontatham The fact that you've had some replies from people who know what you're talking about, and no one seems to have seen this before, makes me think it probably is new.

I guess I was over optimistic about (b), or else those people are slower to reply.

It's a very nice conjecture, and I'm sure no one would object if you were to submit the integer sequence to OEIS.

@simontatham @robinhouston I was at a talk that NJAS gave recently about his favorite sequences and my big takeaway is that his bar for what sequences are interesting enough to be in OEIS is way, way lower than mine.

@simontatham @robinhouston I tried to write a blog article about this, but I couldn't get the tone right. It kepts sounding like a complaint about the riffraff that Sloane permits through the gate, or sneering at someone else's discoveries that I think are inconsequential.

@mjd @robinhouston I must admit that ever since I first saw https://oeis.org/wiki/Examples_of_what_not_to_submit I've had an abiding curiosity about oblong wombat numbers.

(Presumably they fall foul of some rule against crap sequences)

@simontatham @mjd @robinhouston LOL @ "Numbers that I often think about"