[seqfan] RE : Re: Pebble Transform and prime numbers

[Eric Angelini]

Hello Franklin,
I fully agree with you -- it was a simple
suggestion,
Best and sorry for the bandwith waste ;-)
E.

-------- Message d'origine--------
De: seqfan-bounces at list.seqfan.eu de la part de franktaw at netscape.net
Date: jeu. 19/11/2009 21:28
À: seqfan at list.seqfan.eu
Objet : [seqfan] Re: Pebble Transform and prime numbers
 
I have several problems with this.

First (and least), "transform" is usually reserved for operations that 
take one sequence into another (or other kinds of complexes, in other 
contexts).  If you are just taking one number to another, just call it 
a "function".

Second, this takes a nice (finite) sequence/partition transform, and 
makes it an ugly, base-related numeric function.  (Consider for a 
moment what happens to 1234567891.)

Third, the stopping conditions seem very arbitrary.  In particular, 
primes are coming in from left field; there is nothing in the entire 
subject that suggests that looking for primes is a relevant or 
interesting thing to do.

Franklin T. Adams-Watters

-----Original Message-----
From: Eric Angelini <Eric.Angelini at kntv.be>

We could play the same game with the digits inside an integer...

Let's define the "Pebble Transform" (PT) like this:

--------------------------------------
Start with an integer (say '34102')
Define 'd' as the number of non-zero digits (here d=4)
Make every digit minus 1, except for the zero digits (34102
                                                  --> 23001)
Write 'd' ahead of the result (423001)
--------------------------------------

... and now iterate the PT until:
- the resulting integer has more zeros at the end than the one which
  was used for the first PT;
- the resulting integer is a prime

Best,
É.


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