For My Collatz Conjecture get attention because sensed a small Divergent Conjecture characteritics. Anyway was and remain a Rest time times for work .
But over all , for sure I explained it and offered to it a General Character. This make Collatz Conjecture Important for Mathematics.
Any time I was working faster on it, and do not exclude any small errors on, grammatical by writing faster or by fast logic expresions . But supposing Science is a place of free communication , who see it can ask.
To understand Collatz Conjecture , Murgu Conjectures and Murgu Conjecture Vicious Redundancy is the best to follow all matterial below , because in the top is what is new there, and what can be important with Mathematics accepted. This divs will be about a nice and new aspect added by Murgu Conjecture Vicious Redundancy.

Murgu Conjectures Vicious Redundancy, 3 Corners Web Effect. Mathematics Curiosity.

A graphically representation for Murgu Conjecture Vicious Redundancy and for Collatz Conjecture is heavy to make. The Last one was compared with a Tree , and isn't bad , only that, for biggest numbers appear more evidently oscillator characteristic of evolving to root 1. For that I will say wear also an Incomplete Web aspect.

Murgu Conjecture Vicious Redundancy , was named so, because come with 2 or more methaphoric named "roots",
1 , 5 , 17
but I can't exclude as far away to infinity to not be another one or even a "leaf explozion" turning "root" to infinity itself because we demonstrated Infinity Numbers pay respect also for Murgu Conjecture Vicious Redundancy.
Even Collatz Conjecture really is a corner Tree , a half Tree then a incomplete corner Tree Web.
For Murgu Conjecture Vicious Redundancy the oscillator effect became more evidentlly and if represent it only into odd numbers evolution we get 3 corners web representation
AND IMPORTANT ASPECT
SEPARE ODD POSITIVE INTEGERS IN 3

A odd number included into web corner not longer will be meet in another one of remained 2.

Three as Prime Number, Numbers Theory Property.

In, Murgu Conjectures Vicious Redundancy, Collatz Conjecture and Numers Theory is a , to say , lema

For every L pozitive Integer not diect connected to (i∗3):
odd (L=2K+1) we have
1a. (2^L + 1 = 3 x)
and for every L even (L=2K) we have
2a. ((2^L - 1 = 3 y))
, which seem to be a logical property of Number 3, maybe important for Numbers Theory but also for Prime Numbers logic curiosity, but a explanation for Collatz Conjecture and Murgu Conjecture Vicious Redundancy.
Where x and y are also pozitive Integers.

I said then recurence is enough , but to tray to demonstrte it using Recurrence .
L pozitive Integer odd (L=2K+1) we have
1a. (2^L + 1 = 3 x)
If (2^{(2K +1)} + 1 = 3 x)
then also must to be true
(2^{(2K +3)} + 1 = 3 z)
writing (2^{(2K +3)} + 1 = 3 z) as (2²2^{(2K +1)} + 4 -3 = 3 z)
and then as (2²(2^{(2K +1)} + 1) = 3 + 3 z)
that mean
2²(3 x)= 3(z+1)
Demonstration Complete because for (2a.) The Same.
This new property can to born in Numbers Theory a new Contest.
But also can born an appeal. Anyway I didn't saw this property so clear and evedinent as Collatz Conjecture and Murgu Conjectures Vicious Redundancy expose it .
My attraction for Collatz conjecture come from a bit "logic smell" of a Divergent Conjecture , but only a bit.
Also born a new problem :
All Pozitie Integers divisible with 3 pay respect for those lemas related how Collatz Conjecture Evolve starting from a k?
The answer is not and is contained into demonstration. Next pozitive Integer divisible with 3 will be (3x + 3), and next revealed pozitive Integer by lemas will be one from second lema :
(2^(2K+2) - 1 = 3 y)
We know betwen 2^K Integers and 2^(K+1) Integers we have another
2^K Integers , THEN:
FOR EVERY K , WE HAVE NON RESPECT direct FOR LEMAS ANOTHERS :

Then we have now a new property :
(2(K-1)) / 3 as numbers of Integers divisible with 3 between lemas at a Collatz Step.
Murgu Lemas.
Sorry , if I returned second day with any explanations.
Up we demonstrated Infinity Positive Integers pay respect for Collatz Conjecture and Murgu Conjecture Vicious Redundancy . For last even wearing new aspects of new "roots" 5,17 .. , but can answer if far away will be anoter one or more.
When I spoke about NON RESPECT direct to Lemas , is about 3 divisibility folowing Collatz Conjecture, and to remark also 2 new properties :
For every Positive Integer wich can't be write as (i*3) we have:
1. For every odd Integers L - (2^L+1) is divided by 3 .
2. For every even Integers L - (2^L-1) is divided by 3 .
Murgu Lemas
that explain Infinity Numbers pay respect for Collatz Conjecture and Murgu Conjecture Vicious Redundancy
as Number 3 Properties into NUMBER THEORY.
Those 2 Lemas explain also Collatz Conjecture , but explanation to be complete, also Murgu Conjectures and down logical explanation Complete it.
Between 2 Consecutive numbers divisible with 3 do not exist another divisible with 3 , and it is contained also in Lemas.