# [seqfan] Fwd: Re: Balanced / Unbalanced numbers

Éric Angelini bk263401 at skynet.be
Sun Dec 9 17:04:03 CET 2018

```Hello Neil,
thank you for yr interest in this idea!

... what would you suggest?
To keep the smallest Balanced, for instance?
If yes, I'll correct the user's manual!

***WARNING***
Jean-Marc tested his search program this morning
with the "3" start and encountered a "strange
situation" -- quoted in French here (my translation
below):

> Par exemple, en partant de 3, après une cinquantaine d'itérations, on
> arrive à 7693379096578803 qui a une somme paire de 28 et une somme impaire
> de 62, avec peu d'impairs en fin de nombre. Le plus proche Balanced est
> alors à des centaines de milliers de distance, donc long à trouver, et le
> phénomène s'aggrave rapidement avec la taille des nombres.

« Starting with 3 we arrive around the 50th iteration
on 7693379096578803 which has an even sum of 28 and an odd sum of 62,
with very few odd digits at the end of the number. The closest Balanced is
at hundreds of thousands away, so long to find, and the phenomenon gets
quickly worse with the size of the numbers. »

Best,
É.

> ---------- Message d'origine ----------
> De : Neil Sloane <njasloane at gmail.com>
> À :  Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Date : 9 décembre 2018 à 16:40
> Sujet : [seqfan] Re: Balanced / Unbalanced numbers
>
> I liked it a lot until I came to the point about "if there are two choices,
> 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 ?
>
> I guess 199 is the smallest number that has two equi-distant balanced
> neighbors
>
> 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.
> Email: njasloane at gmail.com
>
>
>
> 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 and "Unbalanced" the others.
> >
> > [http://oeis.org/A036301
> > "Numbers n such that sum of even digits of n equals sum of odd digits of
> > n."]
> >
> > 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?
> >
> > Example with the Unbalanced "1":
> > 1 + 112 = 113
> > 113 + 112 = 225
> > 225 + 211 = 436
> > 436 + 431 = 867
> > 867 + 871 = 1738
> > 1738 + 1744 = 3482
> > 3482 + 3476 = 6958 is Balanced.
> >
> > Example with the Unbalanced "2":
> > 2 + 112 = 114
> > 114 + 112 = 226
> > 226 + 211 = 437
> > 437 + 431 = 868
> > 868 + 871 = 1739
> > 1739 + 1744 = 3483
> > 3483 + 3489 = 6972
> > 6972 + 6963 = 13935
> > 13935 + 14003 = 27938
> > 27938 + 27968 = 55906
> > 55906 + 55820 = 111726
> > 111726 + 111728 = 223454
> > 223454 + 223449 = 446903
> > 446903 + 446905 = 893808
> > 893808 + 893813 = 1787621 is Balanced.
> > (if I made no mistakes)
> >
> > P.-S.
> > If there are two possible Balanced to be added to an Unbalanced (as this
> > Unbalanced would stand at the same distance of the two Balanced) compute
> > both branches.
> > Best,
> > É. at Brussels time and day 19:29 Dec 7, 2018
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/

```