[seqfan] Re: Balanced / Unbalanced numbers

[Éric Angelini]

Maximilian wrote :

> replace "closest" by "next larger"

... good point!

> the nearest balanced number is 0,

... aaaarghhh, this guy is too clever!
(I mean Zak:
>> https://oeis.org/A036301
>> Zero added by Zak Seidov, Nov 22 2010)

;-D
Best (and thanks, Maximilian)
É.


>
> ---------- Message d'origine ----------
> De : "M. F. Hasler" <seqfan at hasler.fr>
> À :  Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Date : 9 décembre 2018 à 22:58
> Sujet : [seqfan] Re: Balanced / Unbalanced numbers
> 
> 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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