[seqfan] Re: Worry about old sequence, A030077, paths in K_n

Sean A. Irvine sairvin at gmail.com
Sat Apr 2 21:00:21 CEST 2022

```I get a(15) = 14539 (different from the existing value in the sequence).

I also get A007874(15) = 18218 which is also slightly larger than the
existing value.

In both sequences a(1)-a(14) match the existing values.

On Sun, 3 Apr 2022 at 02:04, David Applegate <david at bcda.us> wrote:

> I worry about using floating point (extended or not) to check if
> different sums of square roots are equal or not.  Using finite precision
> for this is extremely tricky This is a notoriously hard problem in
> general.  For example, to see that
> sqrt(7)+sqrt(14)+sqrt(39)+sqrt(70)+sqrt(72)+sqrt(76)+sqrt(85) !=
> sqrt(13)+sqrt(16)+sqrt(55)+sqrt(67)+sqrt(73)+sqrt(79) you already need
> more than double-precision floating point (their difference is 10^-19,
> see
>
> http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.156.3838&rep=rep1&type=pdf
> ).
> There is a randomized polynomial time algorithm for testing equality,
> but it isn't just compute the result to enough precision.
>
> Some links with additional information:
>
> https://cstheory.stackexchange.com/questions/79/problems-between-p-and-npc/4010#4010
> https://topp.openproblem.net/p33
>
> https://refubium.fu-berlin.de/bitstream/handle/fub188/18449/1993-13.pdf;jsessionid=89F489131478714C98250CFA34AFBFE7?sequence=1
>
> -Dave
>
> On 4/2/2022 5:05 AM, Sean A. Irvine wrote:
> > So far I can verify to A030077(14):
> >
> > 2022-04-02 21:46:54 1
> > 2022-04-02 21:46:54 1
> > 2022-04-02 21:46:54 1
> > 2022-04-02 21:46:54 3
> > 2022-04-02 21:46:54 5
> > 2022-04-02 21:46:54 17
> > 2022-04-02 21:46:54 28
> > 2022-04-02 21:46:54 105
> > 2022-04-02 21:46:54 161
> > 2022-04-02 21:46:54 670
> > 2022-04-02 21:46:55 1001
> > 2022-04-02 21:47:00 2869
> > 2022-04-02 21:47:58 6188
> > 2022-04-02 22:01:58 26565
> >
> > I adapted my existing program for A007874 to this case.  I'm not sure
> why I
> > skipped over it before, but perhaps the dihedral group confused me.  The
> > program uses 50 digits of precision for the length determination. I feel
> > like it should be possible to do this without any kind of precision
> limit,
> > but I don't have the time for that now.  I'll leave it running overnight.
> >
> > I'll also start a run for A007874 itself which also has four additional
> > terms with a(15) looking a little suspicious.
> >
> > Sean.
> >
> >
> >
> > On Sat, 2 Apr 2022 at 16:22, Neil Sloane <njasloane at gmail.com> wrote:
> >
> >> To Seq Fans, The creator of an interesting sequence,  A030077, Daniel
> >> Gittelson, submitted 12 terms in 1999, and 4 more terms were added in
> 2007
> >> by a former editor. Daniel G. wrote to me today, expressing doubt about
> the
> >> 4 additional terms.
> >>
> >> He says he interrupted his study of sequences to pursue a medical
> career,
> >> but now that he is retired, he can return to combinatorics.
> >>
> >> It would be nice if someone could verify the terms! (It is not at all
> >> obvious to me how to do this.)
> >>
> >> Neil Sloane
> >>
> >> --
> >> Seqfan Mailing list - http://list.seqfan.eu/
> >>
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>

```

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