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

Sun Aug 2 00:13:40 CEST 2020

I removed one more incorrect b-file and a whole bunch of incorrect
programs. As far as I can see I removed all incorrect programs. Some
programs look okay if I understand them correctly but for those I'm not
100% sure so I left them there. I hope I didn't overlook such a program.
Some sequences could have more Data. Some of them don't have a b-file. No
examples, no xrefs but I thought to keep them for later.

On Sat, Aug 1, 2020 at 10:12 PM David Corneth <davidacorneth at gmail.com>
wrote:

>   Neil, Thanks for your help. I didn't want to shame someone but not only
> Vincenzo's programs and b-files were wrong. Early versions of Harvey Dale's
> programs used the same idea.
> Though Vincenzo also provided some correct b-files lateron. And Harvey
> gave good programs lateron.
> So I'm just extending them to 10000 terms, putting examples and the xrefs.
> Though however we do the xrefs is fine with me.
>
> Georg, Thanks for your offer. For each of them I have a b-file already.
> Indeed, data can be extended. I could do it but if you can help there that
> would be great. If you look at my drafts of sequences with A-number below
> 100000 you'll see the edits I make to sequences. The list of sequences I'm
> looking at is in the xrefs. I could send them to you in a different format
> if that would help.
>
> On Sat, Aug 1, 2020 at 9:48 PM Georg.Fischer <georg.fischer at t-online.de>
> wrote:
>
>> 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/
>> >
>>
>> --
>> Dr. Georg Fischer, Rotteckring 19, D-79341 Kenzingen
>> Tel. (07644) 913016, +49 175 160 7788, www.punctum.com
>>
>> --
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>