[seqfan] Re: Balanced / Unbalanced numbers

[Neil Sloane]

Well, let's exclude 0, and only consider positive numbers!

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, Dec 9, 2018 at 4:59 PM M. F. Hasler <seqfan at hasler.fr> wrote:

> On Sun, 9 Dec 2018, 11:40 Neil Sloane <njasloane at gmail.com wrote:
>
> > I liked it a lot until I came to the point about "if there are two
> choices,
> > follow both branches".
> > So this is a non-deterministic process: you have to keep track of all the
> > descendants - all the children, grandchildren, ... - until one of them
> > finds a happy marriage and produces a balanced child ?
> >
>
> To avoid this, one could simply replace "closest" by "next larger".
>
>
> On Sun, Dec 9, 2018 at 9:54 AM Éric Angelini <bk263401 at skynet.be> wrote:
> >
> > > Hello SeqFans,
> > > let's call "Balanced" the integers of A036301 <http://oeis.org/A036301>
> (Numbers
> > n such that sum of even digits of n equals sum of odd digits of n.)
>
> and "Unbalanced" the others.
> > >
> > > Take an Unbalanced and add to it its closest Balanced;
> > > if the result is Balanced, stop.
> > > If the result is Unbalanced, iterate.
> > >
> > > Question:
> > > Do all Unbalanced end on a Balanced?
>
>
> No. All numbers strictly between 0 and 112 are unbalanced.
> Thus, for all positive numbers less 112/2 = 56, the nearest balanced number
> is 0,
> and you can add it infinitely many times without ever reaching a balanced
> number.
>
> - Maximilian
>
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