# [seqfan] Re: 2-3 sequence puzzle

Bob Selcoe rselcoe at entouchonline.net
Wed Mar 18 15:49:16 CET 2015

```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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>
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>
```