[seqfan] Re: The Ghost Iteration

[M. F. Hasler]

Dear all,

I propose the basic ghost iteration as https://oeis.org/draft/A329200 (rule
A) and https://oeis.org/draft/A329201 (rule B).

Lars or Harvey, if you wish to submit a cycle related sequence, please go
ahead, or tell me and I'll do it.
One could imagine:
- number of iterations until a number is reached for the second time.
- length of final cycle (=1 for fixed points, including 0)
- least element of the final cycle
 (This would give zero for the numbers that end in 0, so it's at the same
time a characteristic function of numbers not ending in 0, but maybe it
would nevertheless be interesting to submit the list of numbers of one or
the other type.)
Further results could be added there to avoid flooding the SeqFan list.

- Maximilian

On Sat, Nov 9, 2019, 14:22 Lars Blomberg <larsl.blomberg at comhem.se> wrote:

> Using the A rule, 101 eventually enters the cycle
> 207
> 198
> 189
> 197
> /Lars
>
> -----Ursprungligt meddelande-----
> Från: SeqFan <seqfan-bounces at list.seqfan.eu> För Éric Angelini
> Skickat: den 9 november 2019 16:50
> Till: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Ämne: [seqfan] The Ghost Iteration
>
> Hello SeqFans,
> Take an integer like 2019.
> We will call "ghost" the concatenation of the absolute differences of its
> digits.
> The ghost of 2019 is thus 218.
> (We don't keep the possible leading zeros of a ghost: for example, the
> ghost of 1186 is 72 (not 072).
>
> The A rule:
> If a ghost is even, add it to the starting integer. Else subtract it. And
> iterate from there.
>
>   2019
> +  218   <-- first ghost
> ------
>   2237
> +   14   <-- second ghost
> ------
>   2251
> +   34   <-- third ghost
> ------
>   2285
> -   63   <-- fourth ghost
> ------
>   2222
> =    0   <-- last and zero ghost
>
> It seems that every integer will have a zero ghost at the end of the
> process.
> [...]
> More explanations on my weblog:
> http://cinquantesignes.blogspot.com/2019/11/the-ghost-iteration.html
> Best,
> É.
>