[seqfan] Re: The Ghost Iteration

[Lars Blomberg]

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.

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