Reverse Collatz
Ernst Berg
As I was writing to Mensanator there is a program here where I explored
a possible reverse.
I wrote that I would share and why not?
Now this C program was a rough draft where I was more interested in a
general answer to the question of its it possible to work backwards to
generate a large value from a smaller one and the answer is yes it is.
How this will apply as a "reverse collatz" is open to all since ai am not
laying claim to a proper reverse 3x+1,x2 ( Collatz Conjecture )
The first thing is to as if there has already been a reverse
accomplished.
If not then what I have written may serve as an entry or a reference for
a proper work.
I submit all code and works I submit here as covered under GNU public
license. http://www.gnu.org/licenses/gpl.html
So Mensanator I'd guess you have not heard about any reverse. I haven't.
Anyone else? I'll stand by for reply.
--
-*- Symbolism - Logic - Math -*- Three Amigos : Walk Like An Egyptian -*-
Probability states if it is a possibility sooner or later it will happen.
Mensanator
> As I was writing to Mensanator there is a program here where I explored
> a possible reverse.
> I wrote that I would share and why not?
>
> Now this C program was a rough draft where I was more interested in a
> general answer to the question of its it possible to work backwards to
> generate a large value from a smaller one and the answer is yes it is.
>
> How this will apply as a "reverse collatz" is open to all since ai am not
> laying claim to a proper reverse 3x+1,x2 ( Collatz Conjecture )
>
> The first thing is to as if there has already been a reverse
> accomplished.
> If not then what I have written may serve as an entry or a reference for
> a proper work.
>
> I submit all code and works I submit here as covered under GNU public
>
> So Mensanator I'd guess you have not heard about any reverse. I haven't.
I've been using rerse rules since day one. I originally
developed my Hailstone Function by looking
at the reverse sequence from 31 back to 27 to
try and learn something about Mersene Numbers.
>
> Anyone else? I'll stand by for reply.
How does your program work? How do you
decide which rule to use when there are two
possible reverse answers (such as 5 or 32 for 16)?
How do you decide how far to take the
sequence? And yes, getting a larger number
is easy when going in reverse, but have you
investigated the 3-adic chains
of 1mod3 numbers to try and get the
smallest possible number for a given
sequnce length?
Danny73
> As I was writing to Mensanator there is a program here where I explored
> a possible reverse.
> I wrote that I would share and why not?
>
> Now this C program was a rough draft where I was more interested in a
> general answer to the question of its it possible to work backwards to
> generate a large value from a smaller one and the answer is yes it is.
>
> How this will apply as a "reverse collatz" is open to all since ai am not
> laying claim to a proper reverse 3x+1,x2 ( Collatz Conjecture )
>
> The first thing is to as if there has already been a reverse
> accomplished.
> If not then what I have written may serve as an entry or a reference for
> a proper work.
>
> I submit all code and works I submit here as covered under GNU public
>
> So Mensanator I'd guess you have not heard about any reverse. I haven't.
>
> Anyone else? I'll stand by for reply.
>
> --
> -*- Symbolism - Logic - Math -*- Three Amigos : Walk Like An Egyptian -*-
> Probability states if it is a possibility sooner or later it will happen.
The reversal is a much more complex coding problem
because there are --->oo many possible path choices for
each odd (non) 0(mod 3) integer >1.
If the integer is even that is chosen and when -1 is
applied to this integer and it makes it an odd 0(mod 3) integer,
then when divided by 3 it also becomes an even integer that
is also a 0(mod 3) that ends that path sequence.
It ends because only the doubling of this 0(mod 3)only
creates 0(mod 3) integers--->oo.
So I believe the criteria for any path reversal should be
the shortest path from any (non) 0(mod 3) odd too any
odd 0(mod 3) integer.
eg:
Chosen seed = 53
53*2 =106
Path choice =
212,35
Path choice =
424,70
Path choice =
848,140,141,23
So seed 53 has the shortest reversed seed path
that terminates @ 141 because 141==0(mod 3) giving
53 a reverse path length of (5).
53,106,212,424,141 = path length (5)
So what would be the point in finding possibly --->oo
number of different paths for integer (53)
choices with a larger number of paths?
Maybe one reason would be looking for certain binery
patterns.
It appears (1 or 7)(mod 18) pures have longer reverse minimum
path lengths then (5 or 11 or 13 or 17)(mod 18) impures.
eg.
Seed choice =109 pure.
(pure) defined as no smaller integer than 109
can produce 109 in its forward seed path.
109*2 = 218
path choice =
436
path choice =
872,145
path choice =
1744,290
path choice =
3488,581,580
path choice =
6976,1162,1160,193
path choice =
13952,2324,2320,387,386
Terminating @ 387
Path length =
109,218,436,872,1744,581,1162,387 = (8)
Where (8) is the shortest reverse path length for (109).
Dan
Ernst Berg
cool! I will get to posting that in a day or so. There is a project I
have to do.
I think my program is less sophisticated than what you accomplished but
hopefully it be a good topic and add to.
Oh I watched a video on python and it's different than C for sure.
I will get to posting code and details in a day or so.
I will respond to each question in as much detail as possible after I
finish this project I have.
Ernst Berg
Thanks Dan.
I apologize for the delay.
Indeed I agree that there are many paths.
So my work is simple but I need to put it up and will do so as a reply
my reply to Mensanator's reply.
I hope this simulates a conversation for all.
Ernst