[seqfan] Re: Balanced / Unbalanced numbers

[Neil Sloane]

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 ?

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.
Phone: 732 828 6098; home page: http://NeilSloane.com
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
>
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