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

Sun Aug 2 02:44:11 CEST 2020

Another way used in the OEIS to deal with such cases is to put the complete list in one sequence; the others then cross-ref back to that one.

Franklin T. Adams-Watters

-----Original Message-----
From: Hugo Pfoertner <yae9911 at gmail.com>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Sent: Sat, Aug 1, 2020 2:16 pm
Subject: [seqfan] Re: Numbers that are the sum of x nonzero y-th powers

Shouldn't the huge new list of cross-references better go into a (new?)
section (Sum of m nonzero nth powers) in the index? The new X-Ref list will
result in all the sequences it contains being displayed every time you
search for a single A number from this list. I find that rather unfavorable.
Best regards
Hugo Pfoertner

On Sat, Aug 1, 2020 at 8:10 PM Neil Sloane <njasloane at gmail.com> wrote:

> 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/
>

--
Seqfan Mailing list - http://list.seqfan.eu/