[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
add cross-references linking all three (yours, A185969, A248907) (I mean,
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.
Phone: 732 828 6098; home page: http://NeilSloane.com
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
>
>
>  Dear Vladimir,
>>
>> thanks for this nice challenge!
>>
>> My solution: it's a permutation of 2-3 numbers based on your
>> https://oeis.org/A185969
>>
>> Please have a look at draft https://oeis.org/draft/A248907 and add some
>> 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?
>>>
>>> --
>>> Vladimir
>>>
>>> _______________________________________________
>>>
>>> Seqfan Mailing list - http://list.seqfan.eu/
>>>
>>>
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>>
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