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

rayjchandler at sbcglobal.net rayjchandler at sbcglobal.net
Fri Oct 14 23:27:09 CEST 2022

Good first step. 

-----Original Message-----
From: SeqFan <seqfan-bounces at list.seqfan.eu> On Behalf Of Max Alekseyev
Sent: Friday, October 14, 2022 3:21 PM
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Subject: [seqfan] Re: unique primes: should A040017 and A051627 be

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.


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

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