# [seqfan] Re: 2-3 sequence puzzle

Wed Mar 18 16:35:02 CET 2015

```Yes, you are right!

While generating several first elements of this sequence is easy, it
becomes more difficult as we move further, because it involves numbers that
are unfeasible to compute in explicit form, and we need some tricks to
compare them.

Can anybody suggest a program than can generate n-th term of this sequence?

--
Thanks

On Wed, Mar 18, 2015 at 7:49 AM, Bob Selcoe <rselcoe at entouchonline.net>
wrote:

> Hi Vladimir, Reinhard and Seqfans,
>
> More specifically than simply a permutation of 2-3 numbers, isn't this the
> sequence of power towers in ascending order using all permutations of 2s
> and 3s?
>
> 2
> 3
> 2^2 = 4
> 2^3 = 8
> 3^2 = 9
> 2^(2^2) = 16
> 3^3= 27
> 3^(2^2) = 81
> 2^(2^3) = 256
> 2^(3^2) = 512
> ...
>
> This would make a nice OEIS entry (it's not already there!).
>
> Best,
> Bob Selcoe
>
> --------------------------------------------------
> From: "Reinhard Zumkeller" <reinhard.zumkeller at gmail.com>
> Sent: Wednesday, March 18, 2015 6:11 AM
> To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
> Cc: <seqfan at seqfan.eu>
> Subject: [seqfan] Re: 2-3 sequence puzzle
>
>
>>
>> thanks for this nice challenge!
>>
>> My solution: it's a permutation of 2-3 numbers based on your
>> https://oeis.org/A185969
>>
>> substance and a more explicit definition; the provisional definition
>> should
>> be just a comment.
>>
>> Best regards
>> Reinhard
>>
>>
>> 2015-03-18 0:11 GMT+01:00 Vladimir Reshetnikov <v.reshetnikov at gmail.com>:
>>
>>  Dear Seqfans,
>>>
>>> Here is a sequence consisting of all non-empty finite strings of digits 2
>>> and 3 without any duplicates. It begins as:
>>>
>>> 2, 3, 22, 23, 32, 222, 33, 322, 223, 232, 323, 332, 2222, 3222, 233, 333,
>>> 2322, 3322, 2223, 3223, 2232, 3232, 2323, 3323, 2332, 3332, 22222, 32222,
>>> 23222, 33222, 2233, 3233, 2333, 3333, 22322, 32322, 23322, 33322, 22223,
>>> 32223, 23223, 33223, 22232, 32232, 23232, 33232, 22323, 32323, 23323,
>>> 33323, 22332, 32332, 23332, 33332, 222222, 322222, 232222, 332222,
>>> 223222,
>>> 323222, 233222, 333222, 22233, 32233, 23233, 33233, 22333, 32333, 23333,
>>> 33333, 222322, ...
>>>
>>> Can you guess the order in what they appear?
>>>
>>> --
>>>
>>> _______________________________________________
>>>
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>>>
>>>
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```