[seqfan] Re: K(n)—>a(n).

[Neil Sloane]

> For integer n let K(n) be the permutation of the digits of n formed by
sequentially combining the greatest and smallest digits in adjacent pairs
...

I have to say that this sentence makes me feel ill.  There are better
things to think about than playing with the digits of n.

Unless you want to generate more examples for the "Examples of what not to
submit" list.


On Tue, Dec 10, 2019 at 10:32 AM David Sycamore via SeqFan <
seqfan at list.seqfan.eu> wrote:

> Mistake; a(13)=63 not 9. Hope there are no more....
> David.
>
> > On 10 Dec 2019, at 14:29, David Sycamore via SeqFan <
> seqfan at list.seqfan.eu> wrote:
> >
> > For integer n let K(n) be the permutation of the digits of n formed by
> sequentially combining the greatest and smallest digits in adjacent pairs
> until running out of digits to play with. Examples: K(1)=1, K(10)=10,
> K(123)= 312, K(277272)=727272, K(539204)=905243.
> >
> > (Definition is draft, suggestions to improve it are  welcome).
> >
> > We compute a(n) as follows:
> > Take the absolute difference |n-K(n)| to get a new number. Repeat the
> process with that number until reaching a number m for which K(m)=m, then
> a(n)=m.
> >
> > I get (by hand, so could be some bugs)
> >
> > 0,1,2,3,4,5,6,7,8,9,10,11,9,9,9,9,9,54,63,72,20,21,22,9,63,9...
> >
> > Could there be some n for which the above trajectory loops? If so then
> how to define a(n)? (I have not found any such n yet..).
> >
> > A curious feature seems to be that if a(n) is other than n, then it is a
> multiple of 9, but I have not confirmed the veracity of this.
> >
> > Sequence does not seem to be in oeis
> >
> > Any interest in this?
> > Best
> > David.
> >
> > ps: Unless I am  mistaken a(123)=63, a(1234)=81, a(4321)=63,
> a(12345)=70434.
> >
> >
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
>
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>