On Tue, 17 May 2011 10:29:41 -0700, Danny73 wrote:
> On May 14, 5:39 pm, Ernst Berg <Ernst_B
...@sbcglobal.net> wrote:
>> 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.
> 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
I apologize for the delay.
Indeed I agree that there are many paths.
I hope this simulates a conversation for all.
