[seqfan] Re: Clarifying A112531

[Neil Sloane]

The OEIS can contain both versions, one where
we concatenate the parts, as in A241596,
which obviously breaks down once the parts exceed 10, but is much easier
for humans to use,
and one where we list the individual parts, as in A242628,
which obviously breaks down once the parts exceed 10^10^10^10.

When I want to know if some particular ordering of partitions
has a name, or has been mentioned in a book or a paper, I look up the first
version.

Neil


On Tue, May 20, 2014 at 11:52 AM, <franktaw at netscape.net> wrote:

> That's exactly why we normally enter them as I did in A242628.
>
> There are other sequences in the database that eventually "fail" as
> A241596 does, because they would have digits greater than 9. These
> sequences are in kind of a never-never land - we don't consider them
> finite, but neither can they be indefinitely extended.
>
>
> Franklin T. Adams-Watters
>
> -----Original Message-----
> From: Allan Wechsler <acwacw at gmail.com>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Sent: Tue, May 20, 2014 12:50 am
> Subject: [seqfan] Re: Clarifying A112531
>
>
> I am concerned about the well-definedness of 241596, and in general by the
> whole concept of representing partitions as integers in this manner. What
> is A241596(1024)? "A"?
>
>
> On Mon, May 19, 2014 at 2:42 PM, <franktaw at netscape.net> wrote:
>
>  I went ahead and added A242628, since we normally include partitions
>>
> with
>
>> the individual part sizes, not concatenated.
>>
>>
>> Franklin T. Adams-Watters
>>
>> -----Original Message-----
>> From: Neil Sloane <njasloane at gmail.com>
>> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>> Sent: Mon, May 19, 2014 1:39 pm
>> Subject: [seqfan] Re: Clarifying A112531
>>
>>
>> I added A241596 which gives the partitions in this new order, and I
>>
> edited
>
>> A112531.
>> Thanks to everyone for brilliant detective work!
>>
>>
>> On Mon, May 19, 2014 at 2:16 PM, Neil Sloane <njasloane at gmail.com>
>>
> wrote:
>
>>
>>  I just added it, see A241596.
>>
>>> But I will add Franklin's explanation too
>>>
>>>
>>> On Mon, May 19, 2014 at 2:13 PM, <franktaw at netscape.net> wrote:
>>>
>>>  That looks right.
>>>
>>>>
>>>> This can be defined in terms of the binary expansion. Start with the
>>>> partition [1]. Now process the bits of the number from right to
>>>>
>>> left,
>
>> excluding the leading 1. For a zero bit, increase each number in the
>>>> partition by 1; for a one bit, add a part of size 1.
>>>>
>>>> For example, n=11, binary 1011, we get 1 -> 11 -> 111 -> 222. I will
>>>>
>>>>  add
>>>
>>
>>  this sequence.
>>>
>>>>
>>>>
>>>> Franklin T. Adams-Watters
>>>>
>>>> -----Original Message-----
>>>> From: Aai <agroeneveld400 at gmail.com>
>>>> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>>>> Sent: Mon, May 19, 2014 12:51 pm
>>>> Subject: [seqfan] Re: Clarifying A112531
>>>>
>>>>
>>>> The partitions expand as follows IMO:
>>>>
>>>> 1
>>>> 2 11
>>>> 3 22 21 111
>>>> 4 33 32 222 31 221 211 1111
>>>> etc.
>>>>
>>>> A two step next subsequence of partions based on the previous sub:
>>>>
>>>> first:  increment every digit of the partitons by 1
>>>> second: append a 1 to every partitons
>>>>
>>>> e.g. we have:
>>>>
>>>> 3 22 21 111
>>>>
>>>> then the next subsequence of partitions will be:
>>>>
>>>> 4 33 32 222
>>>> followed by
>>>>
>>>> 31 221 211 1111
>>>>
>>>> combined to
>>>>
>>>> 4 33 32 222 31 221 211 1111
>>>>
>>>>
>>>>
>>>>
>>>>
>>>> On 19-05-14 09:09, Peter Luschny wrote:
>>>>
>>>>  Please help clarifying the definition of the triangular array
>>>>
>>>>> http://oeis.org/A112531
>>>>>
>>>>> Peter
>>>>>
>>>>> _______________________________________________
>>>>>
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>>>>>
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>>>> @@i = Arie Groeneveld
>>>>
>>>>
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>>>
>>> --
>>> Dear Friends, I have now retired from AT&T. New coordinates:
>>>
>>> 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
>>>
>>>
>>>
>>>
>> --
>> Dear Friends, I have now retired from AT&T. New coordinates:
>>
>> 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
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>>
>>
>> _______________________________________________
>>
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> _______________________________________________
>
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>
>
>
> _______________________________________________
>
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>



-- 
Dear Friends, I have now retired from AT&T. New coordinates:

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