[seqfan] Re: Binary Complement Sequences

[Tim Peters]

[Tom Duff <eigenvectors at gmail.com>]
> And it just finished! 425720 takes 87,037,147,316 steps to converge to 0.

Congratulations! I was updating your .png file display as it went
along today, and shared at least part of your excitement in real time
:-)

> (Or my  computer glitched, or I have a bug. I seriously doubt the latter,
> because all my other results match what others have reported.)

I mentioned earlier that I won't believe any result on this before
independent replication, because the chance of _some_  bit-level
hardware glitch is non-trivial after some quadrillions of bit
operations.

Alas, I started my run before I wrote code to save checkpoints along
the way, so if my run ends (e.g., a power outage, or some other need
to reboot) I have to start over. It's currently at about 49.7 billion
steps. but is slower code, and would probably take about a week more
to reach 87 billion.

> I didn't expect this. I really thought it would diverge. This
> seriously indicates that it invariably converges to zero.

Infinity is very large ;-)

> That, not the computation of more values, is the front on
> which we need progress, now.

All clues help. Now the smallest starting value for which I have no
thought-to-be definitive answer is 819991 (already ran all smaller
than that to 0, except for 425720). 819991 is slinging integers around
350,000 bits after about 17.5 billion steps.