[seqfan] Re: A279000 and A279001

Arie Groeneveld agroeneveld400 at gmail.com
Fri Dec 16 18:19:49 CET 2016


Neil,

rereading the arVix paper I found (see page 5 Definition 2.1) the forms 
for the following sequences:

A279194

  J = {(11*h+p)*11^2k-1 | h,k in N and p in {1,3,4,5,9} } U 
{(11*h+q)*11^(2k+1)-1 | h,k in N and q in {2,6,7,8,10} }

A279195

  K = {(11*h+p)*11^(2k+1)-1 | h,k in N and p in {1,3,4,5,9} } U 
{(11*h+q)*11^2k-1 | h,k in N and q in {2,6,7,8,10} }


Best regards
  Arie




Op 15-12-16 om 22:39 schreef Neil Sloane:
> Arie, thanks for that reply!  I did some more editing of all 4 sequences,
> A279000 A279001 A279194 A274195.  I think they are OK now. Thanks to you
> and Lars for pointing out that there were mistakes in A279000 and A279001.
>
> 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 Thu, Dec 15, 2016 at 3:41 PM, Arie Groeneveld <agroeneveld400 at gmail.com>
> wrote:
>
>> I can reproduce A278996, A278997, A278998, and A278999 using the formulas
>> as well as using the program. So in my opinion they are correct.
>>
>> All Axxxx sequences you mentioned are also produced by program Apwen.py
>> except A279000 and A279001. I can't come up with a useful title for seqs
>> A279194 and A279195. I think that you can't say that they are related to
>> A279000 and A279001. They are close though.
>>
>> The only thing I wanted to say is that A279000 and A279001 are most likely
>> not part of the arVix article as quoted in LINKS.
>>
>> BTW the program Apwen.py can be found at :
>> http://www-irma.u-strasbg.fr/~guoniu/papers/p93apwen/
>>
>>
>>
>>
>>
>> Op 15-12-16 om 20:32 schreef Neil Sloane:
>>
>> Arie, I didn't fully understand your last message.
>>> Are  A278996, A278997, A278998, and A278999 correct?
>>>
>>> You say A279000 and A279001 are correct but are not explicitly mentioned
>>> in
>>> the article.  In fact they were my guesses as to what J and K were, based
>>> on the other examples in the paper and the lines:
>>> P = {1, 3, 4, 5, 9},
>>> Q = {2, 6, 7, 8, 10},
>>> J = {0, 2, 3, 4, 8, 11, 13, 14, 15, 19, 21, 22, 24, 25, 26, 30, 33, 35, .
>>> .
>>> .},
>>> K = {1, 5, 6, 7, 9, 10, 12, 16, 17, 18, 20, 23, 27, 28, 29, 31, 32, 34, .
>>> .
>>> .}.
>>>
>>> How should the two new entries A279194 and A279195 be described in the
>>> OEIS?  I don't like to say they are defined as the outputs of certain
>>> Python programs!
>>>
>>>
>>>
>>>
>>> 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 Thu, Dec 15, 2016 at 1:01 PM, Arie Groeneveld <
>>> agroeneveld400 at gmail.com>
>>> wrote:
>>>
>>> A279194 and A279195are outputs of the python program but differ from the
>>>> next sequences.
>>>> A279000 and A279001 are according the form in the title. But I don't see
>>>> them mentioned in the paper or I missed them.
>>>>
>>>> AFAICS A278996, A278997, A278998, and A278999 are indeed outputs of
>>>> Apwen.py for arguments 3 and 5 or generated by the forms in the titles.
>>>>
>>>> So the only question for me is: where are A279000 and A279001 mentioned
>>>> in
>>>> the arVix paper.
>>>>
>>>>
>>>> Op 15-12-16 om 18:16 schreef Neil Sloane:
>>>>
>>>> There are now four sequences:
>>>>
>>>>> A279000 and A279001, which Lars Blomberg has corrected, and
>>>>> A279194 and A279195, which are the sequences J and K on page 10
>>>>> of the arXiv paper, but whose definitions are not clear to me.
>>>>>
>>>>> Arie Groeneveld, can you give me definitions for A279194 and A279195?
>>>>>
>>>>> And what about the earlier sequences that I added: A278996, A278997,
>>>>> A278998, and A278999. Are they OK?  Now I am worried!
>>>>>
>>>>>
>>>>> 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 Thu, Dec 15, 2016 at 11:00 AM, Arie Groeneveld <
>>>>> agroeneveld400 at gmail.com>
>>>>> wrote:
>>>>>
>>>>> Examining the article, this is what I read:
>>>>>
>>>>>> The numbers mentioned in para 2.3 are the output of program Apwen.py
>>>>>> for
>>>>>> argument 11 (function F11(x)) and not of the form:
>>>>>>
>>>>>> (11*h+j)*11^k-1 for h,k in N and j in {1,3,4,5,9} or {2,6,7,8,10}
>>>>>>
>>>>>> One can check this by running the Python program.
>>>>>>
>>>>>> At preceding para's 2.1 and 2.2 alternative expressions (not only
>>>>>> different in values 3 and 5but also in sets for j) are shown for
>>>>>> functions
>>>>>> F3(x) and F5(x), which are outputs of Apwen.py 3 and Apwen.py 5p. In
>>>>>> para
>>>>>> 2.3 no such expression is shown for the two sequences (is it not
>>>>>> found?).
>>>>>>
>>>>>> So if one refers to the article for both sequences the titles are
>>>>>> wrong.
>>>>>>
>>>>>>
>>>>>> Thanks
>>>>>>
>>>>>>
>>>>>>
>>>>>> Op 15-12-16 om 08:33 schreef Lars Blomberg:
>>>>>>
>>>>>>
>>>>>> The names seem to be wrong.
>>>>>>
>>>>>>> Using the given formulas, the data is not reproduced and the two
>>>>>>> sequences
>>>>>>> are not each others complement.
>>>>>>>
>>>>>>> Refer to section 2.3 in the paper.
>>>>>>>
>>>>>>> Although not explicitly stated there, I guess that 5 in the formulas
>>>>>>> should
>>>>>>> be replaced by 11.
>>>>>>>
>>>>>>> Now A279000 and A279001 are complements of each other.
>>>>>>>
>>>>>>> But still, it seems that some values in the paper have been placed in
>>>>>>> the
>>>>>>> wrong sequence:
>>>>>>>
>>>>>>> A279001 contains 10 = (11*0+1)*11^1-1 that belongs to A279000 with
>>>>>>> (h,j,k)=(0,1,1).
>>>>>>>
>>>>>>> A279000 contains 21 = (11*0+2)*11^1-1 that belongs to A279001 with
>>>>>>> (h,j,k)=(0,2,1).
>>>>>>>
>>>>>>> A279001 contains 32 = (11*0+3)*11^1-1 that belongs to A279000 with
>>>>>>> (h,j,k)=(0,3,1).
>>>>>>>
>>>>>>>
>>>>>>> /Lars Blomberg
>>>>>>>
>>>>>>>
>>>>>>> --
>>>>>>> Seqfan Mailing list - http://list.seqfan.eu/
>>>>>>>
>>>>>>>
>>>>>>> --
>>>>>> Seqfan Mailing list - http://list.seqfan.eu/
>>>>>>
>>>>>> --
>>>>>>
>>>>> Seqfan Mailing list - http://list.seqfan.eu/
>>>>>
>>>>>
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>>> Seqfan Mailing list - http://list.seqfan.eu/
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>>
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>> Seqfan Mailing list - http://list.seqfan.eu/
>>
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