[seqfan] Re: The Annoyance Sequence

[Allan Wechsler]

Jay, that's way more work than I expected anybody to put into this, but
it's extremely interesting! (Obligatory possible sequence: # of steps to
eliminate n, or -1 if n is provably never eliminated.)

On Sat, Jul 22, 2023 at 7:06 PM Jay Anderson <horndude77 at gmail.com> wrote:

> On Thu, Jul 20, 2023 at 10:22 PM Jay Anderson <horndude77 at gmail.com>
> wrote:
>
> > On Thu, Jul 20, 2023 at 7:11 AM Allan Wechsler <acwacw at gmail.com> wrote:
> >
> >> Could it be that 5 is the only number that never appears?
> >>
> >
> > I believe 55 also gets in a loop. Here's the loop 5 gets is in:
> >
> > ...
> >
> > 1189 is likely to be the next one never to appear, but I haven't thought
> > about that one.
> >
>
> I ran the sequence through the first 4,000,000 entries. I had it print the
> 10 smallest entries not in the output of the sequence yet every 100,000
> entries. Here's the end:
>
> ...
>  3500000: Some(4399409)
> minimums: [5, 55, 1189, 467389, 485938, 495550, 507117, 521792, 538680,
> 558382]
> 3600000: Some(4524984)
> minimums: [5, 55, 1189, 485938, 495550, 521792, 538680, 558382, 573837,
> 575213]
> 3700000: Some(4650600)
> minimums: [5, 55, 1189, 495550, 538680, 558382, 573837, 575213, 576699,
> 589451]
> 3800000: Some(4776256)
> minimums: [5, 55, 1189, 558382, 573837, 575213, 576699, 589451, 591294,
> 602331]
> 3900000: Some(4902012)
> minimums: [5, 55, 1189, 573837, 575213, 576699, 589451, 591294, 602331,
> 622080]
> 4000000: Some(5027748)
> minimums: [5, 55, 1189, 576699, 589451, 591294, 602331, 631684, 633176,
> 647466]
>
> So 5, 55, and 1189 will never make it out (1189 needs a proof to be sure).
> After that there is no obvious entry that repeats. It also seems likely
> that these are the only 3, but I'm not sure how you'd show that.
>
> -----Jay Anderson
>
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