[seqfan] Re: Binary Complement Sequences

[Allan Wechsler]

It would be worthwhile comparing the trajectory plots of 819991 with those
for 425750. For all we know, the trajectories merge around the seventeen
millionth step, and if they do, it won't be necessary to run 819991 to
completion. In fact, 819991 might be an early iterate of 425750.

On Tue, Dec 27, 2022 at 1:35 PM Tim Peters <tim.peters at gmail.com> wrote:

> [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.
>
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