[seqfan] Re: Matiyasevich's Dual Eratosthenes Sieve

[Allan Wechsler]

If I understand what Matiyasevich is doing in the "dual sieve" slides, at
the nth step he retains only multiples of n.

If that's right, then the sequence that develops along the left edge of his
table is oeis.org/A003418.

On Mon, Dec 18, 2023 at 7:32 PM Neil Sloane <njasloane at gmail.com> wrote:

> To Sequence Fans
>
> On Dec 14 2023 the legendary Yuri Matiyasevich (*) gave a Zoom talk at
> Rutgers where he briefly mentioned
>
> (towards the end of his talk)
>
> the Dual Eratosthenes Sieve.
>
>
> You can see his slides here:
>
> https://sites.math.rutgers.edu/~zeilberg/expmath/yuri23.pdf
>
> Normally a video of his talk would appear here:
>
> https://sites.math.rutgers.edu/~zeilberg/expmath/archive23.html
>
> but maybe it hasn't been posted yet.
>
>
> Now the classical E. sieve is the source for many sequences in the OEIS,
>
> for example A083221. So perhaps the Dual E. Sieve will be too.
>
> I don't have time to explore this, so I'm asking the Sequence Fans for
> help.
>
>
> Y. M. gave a talk about it in 2021 at St Petersburg State U.,
>
> entitled New Life for an Old Sieve, see the announcement
>
> https://math-cs.spbu.ru/en/news/a-new-life-of-the-old-sieve/
>
>
> During his Rutgers talk he gave the following places to look for further
> information (on his website):
>
> https://logic.pdmi.ras.ru/~yumat
>
>
> https://logic.pdmi.ras.ru/~yumat/publications/publications.php?istate=state_show_paper&imykey=94&ilang=eng
>
>
> https://logic.pdmi.ras.ru/~yumat/publications/publications.php?istate=state_show_paper&imykey=98&ilang=eng
>
>
> https://logic.pdmi.ras.ru/~yumat/publications/publications.php?istate=state_show_paper&imykey=99&ilang=eng
>
>
> Possibly a search in MSN or ZBL for Matiyasevich and Dual Eratosthenes
> Sieve would turn up something.
>
>
> (*) Said to be the only person still alive who solved one of Hilbert's
> problems.
>
>
> 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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>