[seqfan] Re: The Annoyance Sequence

[Jay Anderson]

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