[seqfan] Re: Ali Sada's A364054

[Allan Wechsler]

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
>
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