# [seqfan] Re: 2-3 sequence puzzle

Neil Sloane njasloane at gmail.com
Wed Mar 18 18:02:03 CET 2015

```Bob, that's very nice, your "towers" sequence - please submit it, and
make sure each one points to the other two)

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Email: njasloane at gmail.com

On Wed, Mar 18, 2015 at 10:49 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?
>>>
>>> --
>>>
>>> _______________________________________________
>>>
>>> Seqfan Mailing list - http://list.seqfan.eu/
>>>
>>>
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```