[seqfan] Re: Strong Law of Small Numbers and the "Sequence in Context".
charles.greathouse at case.edu
Mon Oct 17 02:37:29 CEST 2016
Often with computers we can compute enough terms of a sequence that the
chance of a match being coincidence is infinitesimal. But as in Brad's
example, there are mathematical reasons that sequences could be close
without being the same. Still, when I come across a conjecture I usually
code a quick test to see if there is numerical support (or counterexamples)
-- it's too easy with lots of cheap compute power today.
Case Western Reserve University
On Sat, Oct 15, 2016 at 11:10 AM, <bradklee at gmail.com> wrote:
> Hi Antti and Jean-Paul,
> Thanks for bringing up this article, especially the tone of it, very
> timely; though, maybe the title should be "Strong arm of small numbers."
> A few comments on relevancy to OEIS:
> 1. Though contrived, the natural number solutions of
> x+y+m*z = n
> Will only diverge from solutions of
> x+y = n
> After n >= m. Guy's Ex. 29 ( https://oeis.org/A180445 ) is similar, and
> there are many examples in the OEIS of these sequences, which are also
> noteworthy in physics, with applications dating back to H.A. Bethe himself.
> I also think that Guy's examples 24,25, and 26 are worth a review. It's
> not always clear that functions involving division will turn out to be
> integer sequences. This is one reason that Pascal's triangle fits so nicely
> into the OEIS, because it just involves more and more multiplication or
> addition as you go through the rows.
> So over here the strong arm of numbers is saying something along the lines
> "double check your assumptions before making a submission".
> Since I am already being attacked for "muddy" writing and low standards, I
> am pretty horrified that someday I will make a mistake in my calculations,
> have a sequence defamed, and then end up in so-and-so's gulag. Happened to
> Landau, read about it on the former KGB freedom of information. It's out
> > On Oct 15, 2016, at 7:27 AM, jean-paul allouche <
> jean-paul.allouche at imj-prg.fr> wrote:
> > Hi; is this link useful then?
> > http://www.maa.org/sites/default/files/pdf/upload_
> > best
> > jean-paul
> >> Le 15/10/16 à 10:49, Antti Karttunen a écrit :
> >> Regarding Guy's Strong Law of Small Numbers
> >> (see e.g. https://en.wikipedia.org/wiki/Strong_Law_of_Small_Numbers
> >> for a brief summary. I also had the paper printed/photocopied once,
> >> but I cannot find them now to check how much Wikipedia abridges or
> >> distorts its message)
> > --
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