[seqfan] Re: unique primes: should A040017 and A051627 be truncated?

[Max Alekseyev]

Rather than do truncation, I've changed the definition to unambiguously
match the listed terms, and added a comment about under what (unproved)
assumption A040017 represents a sorted version of A007615.

Regards,
Max

On Thu, Oct 13, 2022 at 2:11 PM Max Alekseyev <maxale at gmail.com> wrote:

> SeqFans,
>
> We have well-defined sequences A007498 and A007615 that list smallest
> known periods and the corresponding unique primes, respectively. These
> sequences are in order (unless there was a computational error).
>
> The related sequence A040017 makes an attempt to sort the terms of
> A007615, however as soon as the terms become big we lose guarantee that
> there are no unknown primes appearing in between of the known ones.
> That is, the currently listed terms of A040017 and its counterpart A051627
> become conjectural at best.
>
> Using the largest known term of A007498, which is 198552, we have a
> guarantee that all unique primes below it are known. Perhaps, we can push
> this bound a bit further, but I highly doubt we can compute all unique
> primes below, say, (10^19-1)/9 currently listed as A040017(13).
>
> Do I miss something?
> If not, both A040017 and A051627 should be truncated to guaranteedly known
> initial terms.
>
> Regards,
> Max
>
>
>