[seqfan] Re: Numbers that are the sum of x nonzero y-th powers
David Corneth
davidacorneth at gmail.com
Sun Aug 2 19:40:09 CEST 2020
You're welcome Harvey. I only found out through documentation but I can't
write Mathematica so rewriting them would feel too ambitious.
Best,
David
On Sun, Aug 2, 2020 at 4:18 PM Harvey P. Dale <hpd at hpdale.org> wrote:
> David:
>
> Thanks for catching and fixing my Mma programs that were in
> error.
> Best,
> Harvey
>
>
>
> -----Original Message-----
> From: SeqFan <seqfan-bounces at list.seqfan.eu> On Behalf Of David Corneth
> Sent: Saturday, August 1, 2020 4:13 PM
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Subject: [seqfan] Re: Numbers that are the sum of x nonzero y-th powers
>
>
>
> 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
> <mailto: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:
>
> > > https://urldefense.proofpoint.com/v2/url?u=http-3A__NeilSloane.com&d
>
> > > =DwICAg&c=slrrB7dE8n7gBJbeO0g-IQ&r=XiYos0f3ggKs3-anzJfncQ&m=RGNf2EfZ
>
> > > F3UPK0kyhVn2rp_qFN3zr9ZerThdFUz29lk&s=fqhUAz3V7DeA4Rbudj_r81oY7NPUAK
>
> > > DeT4PCDtuwG5o&e=
>
> > > Email: njasloane at gmail.com<mailto:njasloane at gmail.com>
>
> > >
>
> > >
>
> > >
>
> > > On Sat, Aug 1, 2020 at 1:26 PM Marc LeBrun <mlb at well.com<mailto:
> 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<mailto: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 -
>
> > >>> https://urldefense.proofpoint.com/v2/url?u=http-3A__list.seqfan.eu
>
> > >>> _&d=DwICAg&c=slrrB7dE8n7gBJbeO0g-IQ&r=XiYos0f3ggKs3-anzJfncQ&m=RGN
>
> > >>> f2EfZF3UPK0kyhVn2rp_qFN3zr9ZerThdFUz29lk&s=mcHDB9-BUMh8pJ8rw5Nctk5
>
> > >>> rUVqj1QSbekpaKjz6gts&e=
>
> > >>
>
> > >>
>
> > >> --
>
> > >> Seqfan Mailing list -
>
> > >> https://urldefense.proofpoint.com/v2/url?u=http-3A__list.seqfan.eu_
>
> > >> &d=DwICAg&c=slrrB7dE8n7gBJbeO0g-IQ&r=XiYos0f3ggKs3-anzJfncQ&m=RGNf2
>
> > >> EfZF3UPK0kyhVn2rp_qFN3zr9ZerThdFUz29lk&s=mcHDB9-BUMh8pJ8rw5Nctk5rUV
>
> > >> qj1QSbekpaKjz6gts&e=
>
> > >>
>
> > >
>
> > > --
>
> > > Seqfan Mailing list -
>
> > > https://urldefense.proofpoint.com/v2/url?u=http-3A__list.seqfan.eu_&
>
> > > d=DwICAg&c=slrrB7dE8n7gBJbeO0g-IQ&r=XiYos0f3ggKs3-anzJfncQ&m=RGNf2Ef
>
> > > ZF3UPK0kyhVn2rp_qFN3zr9ZerThdFUz29lk&s=mcHDB9-BUMh8pJ8rw5Nctk5rUVqj1
>
> > > QSbekpaKjz6gts&e=
>
> > >
>
> >
>
> > --
>
> > Dr. Georg Fischer, Rotteckring 19, D-79341 Kenzingen Tel. (07644)
>
> > 913016, +49 175 160 7788,
>
> > https://urldefense.proofpoint.com/v2/url?u=http-3A__www.punctum.com&d=
>
> > DwICAg&c=slrrB7dE8n7gBJbeO0g-IQ&r=XiYos0f3ggKs3-anzJfncQ&m=RGNf2EfZF3U
>
> > PK0kyhVn2rp_qFN3zr9ZerThdFUz29lk&s=Plft_zDAoD89XqOJE3UWbrEfRvGu5dP3N_7
>
> > PdnNWj9M&e=
>
> >
>
> > --
>
> > Seqfan Mailing list -
>
> > https://urldefense.proofpoint.com/v2/url?u=http-3A__list.seqfan.eu_&d=
>
> > DwICAg&c=slrrB7dE8n7gBJbeO0g-IQ&r=XiYos0f3ggKs3-anzJfncQ&m=RGNf2EfZF3U
>
> > PK0kyhVn2rp_qFN3zr9ZerThdFUz29lk&s=mcHDB9-BUMh8pJ8rw5Nctk5rUVqj1QSbekp
>
> > aKjz6gts&e=
>
> >
>
>
>
> --
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> Seqfan Mailing list -
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