[seqfan] Re: A program to compute A002845

[bacher]

Nice. Thank you very much,

Best wishes, Roland Bacher

Vladimir Reshetnikov <v.reshetnikov at gmail.com> a écrit :

> 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
>> >
>> > --
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>>
>>
>>
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>
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