[seqfan] Re: K(n)—>a(n).

[David Sycamore]

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. 
> 
> 
> 
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