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

Neil Sloane njasloane at gmail.com
Sun Aug 2 21:32:31 CEST 2020


Maximilan said (correctly) that

Now we need a global search & replace "are the form of x " ==> " are the
sum of x".

I am willing to do this, but let's wait until all the editing of these
sequences is finished. (Is it already finished?  David?)

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 Sun, Aug 2, 2020 at 2:24 PM David Corneth <davidacorneth at gmail.com>
wrote:

> 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
> >
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> >
> > > >>> f2EfZF3UPK0kyhVn2rp_qFN3zr9ZerThdFUz29lk&s=mcHDB9-BUMh8pJ8rw5Nctk5
> >
> > > >>> rUVqj1QSbekpaKjz6gts&e=
> >
> > > >>
> >
> > > >>
> >
> > > >> --
> >
> > > >> Seqfan Mailing list -
> >
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> >
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> >
> > > >> EfZF3UPK0kyhVn2rp_qFN3zr9ZerThdFUz29lk&s=mcHDB9-BUMh8pJ8rw5Nctk5rUV
> >
> > > >> qj1QSbekpaKjz6gts&e=
> >
> > > >>
> >
> > > >
> >
> > > > --
> >
> > > > Seqfan Mailing list -
> >
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> >
> > > > 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=
> >
> > >
> >
> > > --
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> >
> > > PK0kyhVn2rp_qFN3zr9ZerThdFUz29lk&s=mcHDB9-BUMh8pJ8rw5Nctk5rUVqj1QSbekp
> >
> > > aKjz6gts&e=
> >
> > >
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> >
> >
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