[seqfan] Re: A279000 and A279001

Fri Dec 16 19:03:31 CET 2016

Arie, Thank you very much for that detective work!  I have edited the two
sequences.

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 Fri, Dec 16, 2016 at 12:19 PM, Arie Groeneveld <agroeneveld400 at gmail.com>
wrote:

> 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
>>>>>>>>
>>>>>>>>
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