[seqfan] Re: Clarifying A112531

Allan Wechsler acwacw at gmail.com
Mon May 19 22:15:42 CEST 2014


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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>>>>
>>>>
>>> --
>>> Met vriendelijke groet,
>>> @@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/
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>



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