[seqfan] Re: A program to compute A002845

[Vladimir Reshetnikov]

Yes, I believe there are.

For example, the equality (((x^x)^x)^x)^x = ((x^x)^x)^(x^x) holds for x =
2, but does not hold for x = -0.0802980827... + 4.4082663977... i, although
it satisfies (x^x)^x = x^(x^x).

--
Best regards
Vladimir Reshetnikov


On Wed, Jan 30, 2019 at 6:06 AM bacher <Roland.Bacher at univ-grenoble-alpes.fr>
wrote:

>
> Are there any identities not coming from
> ((2^2)^2)=(2^(2^2)) among such expressions?
>
> Best wishes, Roland Bacher
>
>
> Vladimir Reshetnikov <v.reshetnikov at gmail.com> a écrit :
>
> > Today I published a program on GitHub that computes elements of
> > https://oeis.org/A002845 (Number of distinct values taken by 2^2^...^2,
> > with n 2's and parentheses inserted in all possible ways).
> >
> > https://github.com/VladimirReshetnikov/Oeis.A002845
> >
> > It uses a special representation of numbers that allows to efficiently
> > manipulate high power towers, but is still brute force in the sense that
> it
> > enumerates and stores all possible outcomes for each n. So far I was able
> > to confirm all values currently listed (up to n=27), and I estimate that
> I
> > would need a machine with more than 100GB RAM to compute the next.
> >
> > I would be delighted if anybody could improve my solution, port it to
> other
> > programming languages, or provide computational resources.
> >
> > --
> > Best regards
> > Vladimir Reshetnikov
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
>
>
>
> --
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>