Neil Sloane njasloane at gmail.com
Mon Oct 23 08:17:13 CEST 2023

```Dear Chai Wah, I was not very clear. What I was focusing on were the two
*lowest* lines at any point.  These seem to always be a pair of unbroken
diverging lines of equal length, such that when one pair ends, the next
pair starts.  You new graph shows this very nicely.  If we had a model just
for those lines, it might show something.

Dear Allan, I hope you will create all those sequences you mentioned!

Best regards
Neil

Neil J. A. Sloane, Chairman, OEIS Foundation.
Also Visiting Scientist, Math. Dept., Rutgers University,
Email: njasloane at gmail.com

On Mon, Oct 23, 2023 at 1:44 AM Allan Wechsler <acwacw at gmail.com> wrote:

> As with Recaman's sequence and all similar constructions, the entries
> belong to well-defined "tiers". When you add N times the current modulus,
> the tier number increases by N (with the obvious extension to negative
> values of N.) Additional ideas for ancillary sequences include:
>
> The tier numbers: 1, 2, 3, 4, 3, 4, 3, 4, 5, 6, 5, 6, 5, 6, ...
>
> The index of the first occurence of tier n: 1, 2, 3, 4, 9, 10, 23, 28, ...
>
> The index of the *last* occurrence of tier n: 1, 2, 7, 8, 21, 36, 81, ...
>
> The number of entries in tier n: 1, 2, 3, 3, 7, 13, 27, ...
>
> The value of the last entry of tier n: 1, 3, 2, 19, 12, 13, 8, 21 ...
>
> That last one is of especial interest because if 5 ever occurs, it will be
> in this subsequence. Small entries can only appear close to the extinction
> of a tier.
>
> On Sun, Oct 22, 2023 at 12:46 PM Neil Sloane <njasloane at gmail.com> wrote:
>
> > The definition involves the primes, but otherwise this is quite similar
> to
> > Recaman's A005132.  However, the graph seems a bit simpler than
> Recaman's,
> > since it appears to be dominated by pairs of straight lines, one
> descending
> > and one ascending (as can be seen from Chai Wah Wu's b-file).  5 is still
> > missing even after 10K terms. It would be nice to know more. (I added
> some
> > comments to the entry.)
> >
> > Best regards
> > Neil
> >
> > Neil J. A. Sloane, Chairman, OEIS Foundation.
> > Also Visiting Scientist, Math. Dept., Rutgers University,
> > Email: njasloane at gmail.com
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>
```