[seqfan] Re: Numbers that are the sum of x nonzero y-th powers

Sat Aug 1 21:48:02 CEST 2020

Hi SeqFans,

though it is regrettable that sometimes b-files (VL's, but also
from other people) had incredible typos, cut-and-paste mistakes,
wrong "guessed" generating function terms etc. ...

... I'm not so pessimistic about the overall quality of
the b-files (and terms). By comparing them with the terms
computed by Sean Irvine's jOEIS Java programs we have
checked the vast majority of the sequences below A034000,
most of the LinearRecurrences and GeneratingFunctions,
for a total of 93820 sequences up to now.

@David: I'm interested in helping to fix the problems
in the range A003325-A003399. I'm just running them,
but some take quit some time. I can easily provide b-files
and longer term lists by automatic scripts. So
please let us communicate privately on the procedure.

Regards - Georg

Am 01.08.2020 um 20:10 schrieb Neil Sloane:
> David Corneth,  what you should have said is that the Mathematica program
> in A003345 was written by Vincenzo Librandi, who also contributed the
> b-file.
> 
> I am afraid there have been other cases recently where his b-files have had
> serious errors.
> I have a note from my diary for July 25 2020 saying:
> "Librandi's 1000-term b-file for A092315 had 127 errors - thanks to Gerhard
> Kirchner for catching & correcting them."
> 
> You mentioned  sequences "...starting at about A003325  and going through
> A003400. ..." and that you have corrected versions of b-files for all of
> them.
> 
> That is great!  Yes, we need to correct them, certainly. I temporarily
> raised your edit limit to 30.  If I can do anything else to help let me
> know.  We can also ask the admin guys to help too, if necessary.
> 
> Unfortunately, it looks like Vincenzo Librandi has contributed more than
> 20000 b-files
> 
> Here are the first ten:
> 
> %H A000065 N. J. A. Sloane and Vincenzo Librandi, <a
> href="/A000065/b000065.txt">Table of n, a(n) for n = 0..1000</a> (first 199
> terms from N. J. A. Sloane)
> %H A000115 Vincenzo Librandi, <a href="/A000115/b000115.txt">Table of n,
> a(n) for n = 0..10000</a>
> %H A000155 Vincenzo Librandi, <a href="/A000155/b000155.txt">Table of n,
> a(n) for n = 0..200</a>
> %H A000208 Vincenzo Librandi, <a href="/A000208/b000208.txt">Table of n,
> a(n) for n = 0..1000</a>
> %H A000212 Vincenzo Librandi, <a href="/A000212/b000212.txt">Table of n,
> a(n) for n = 0..5000</a>
> %H A000216 Vincenzo Librandi, <a href="/A000216/b000216.txt">Table of n,
> a(n) for n = 1..100</a>
> %H A000218 Vincenzo Librandi, <a href="/A000218/b000218.txt">Table of n,
> a(n) for n = 1..100</a>
> %H A000221 Vincenzo Librandi, <a href="/A000221/b000221.txt">Table of n,
> a(n) for n = 1..100</a>
> %H A000226 Vincenzo Librandi, <a href="/A000226/b000226.txt">Table of n,
> a(n) for n = 3..200</a>
> %H A000264 Vincenzo Librandi, <a href="/A000264/b000264.txt">Table of n,
> a(n) for n = 1..200</a>
> 
> I don't know how many of the 20000 have been checked. He was blocked from
> contributing to the OEIS in April of  this year.
> 
> 
> 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 Sat, Aug 1, 2020 at 1:26 PM Marc LeBrun <mlb at well.com> wrote:
> 
>> To actually fix it, someone could either
>>     1. change the title to "numbers that are a sum of 7 numbers in 1
>> through 5 raised to the 8th power"
>> or 2. change the sequence values so they actually include all the numbers
>>
>> (I recommend #2, although it's more work).
>>
>> At the very least, some comment should be quickly added to warn users that
>> the sequence as it stands is incorrect.
>>
>>
>>> On Jul 31, 2020, at 4:11 PM, David Corneth <davidacorneth at gmail.com>
>> wrote:
>>>
>>> Hi All,
>>>
>>> I just came across A003385 which is called:
>>> Numbers that are the sum of 7 nonzero 8th powers.
>>>
>>> And there is a whole series of such sequences, starting at about A003325
>>> going through A003400.
>>>
>>> I think at least some but still quite many need the following fixes.
>>> The most important ones are b-files and progs.
>>> A003385 has a b-file of 3432 terms, the largest of them being: 117440512.
>>> However, up to that bound, 3319 terms are missing.
>>> Possibly it's due to the prog at hand, or at least the idea.
>>> The prog there is in Mathematica:
>>> Total/@Tuples[Range[5]^8, 7]//Union
>>> And such progs are all arround those sequences.
>>> Now I don't know Mathematica quite well but I looked in the documentation
>>> and range[5] gives the array [1, 2, 3, 4, 5] and each of these numbers is
>>> going to be raised to the 8th power, giving:
>>> [1, 128, 2187, 16384, 78125]. Then some tuples (5^7 of them) are made and
>>> that makes a list of distinct terms. i.e. duplicates are removed, and
>> there
>>> will be a lot of duplicates; all permutations of a sorted array of 7
>>> numbers each in 1 through 5 raised to the 8th power.
>>>
>>> The first missing term in the b-file is 43046727 which is 1^8 + 1^8  +
>> 1^8
>>> + 1^8  + 1^8  + 1^8  + 9^8.
>>> Now a quick look shows me a lot of these sequences have such progs.
>>> Another one is A003384 which has the Mathematica program:
>>> Union[Total[#^8]&/@Tuples[Range[10], 6]]
>>> same issue.
>>> Some look better, like With[{upto=10000},
>>> Select[Union[Total/@Tuples[Range[Floor[Surd[upto-4, 6]]]^6, 5]],
>> #<=upto&]]
>>> as in correct but perhaps inefficient.
>>> in A003361:  Numbers that are the sum of 5 nonzero 6th powers.
>>> At any rate, I think they need to be revised.
>>>
>>> Some lack a b-file and could have that.
>>> In some sequences, data could be extended to the 260 chars.
>>> And probably they could xref each other more.
>>> And an example or two would be nice.
>>>
>>> What's a good approach here? What changes should actually be made? Who
>> can
>>> help?
>>>
>>> Best,
>>> David
>>>
>>> --
>>> 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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Dr. Georg Fischer, Rotteckring 19, D-79341 Kenzingen
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