I don’t use probability by the way. just thought the numbers as some subsets then permute them to be a simple structure.

I said there are only six(2*3)-typed parent nodes. and finally all odds converge the smallest numbers of each these typed parents.

but more interesting thing is that there are two-kinds of exponent tuples which formed three-forms by the circular shift oparation, respectively.

I only understand the structure of the sequence and how all N reach 1 without using probability. but I can’t give a rigid proof for it. I am very elementary amateur.

]]>https://www.quora.com/Is-the-Collatz-Conjecture-solvable/answer/David-Cole-146 ]]>

I am a real amateur, non-English speaker woman who is hard to conversation in English. but I think I understand well for the “structure” of the sequence than other people, sorry. And how all N; especially such numbers odd<f(odd) finally decrease and reach 1.

However It may be defficult to describe the total stopping time k for all N.

Collatz sequence' structure seems to have some interesting properties which relates other mathematical areas also computer science. Because this sequence can be represented as a rather simple data structure.

2017 is the 80th since L. Collatz have found this fascinate sequence. I hope the problem proved in this year. ]]>

Consider the values of even set {a} and even set {d} where the sets represent the ascending and descending numbers, respectively. They are disjoint sets of elements a (every 3x+1) and elements d (every a divided by 2∗2…).

If 3x+1 is true for every a=4+(6∗k)

(4, 10, 16, 22, 28, 34…)

and

If a/(2∗2…) is true for every d=2+(6∗k)

(2, 8, 14, 20, 26, 32…)

Then, a≠d for ∞

(A Collatz and mn+x calculator/grapher: http://questafi.net/numbers/CollatzCalcNGraph-1.xlsm)

]]>The interesting extension is : either consider the original Collatz (3 n +1) formula extended to negative integers, or; equivalently, study the alternate (3 n -1) variant on the positives.

Anyways, your claim to a proof for the “classical” Collatz problem on the positives would be a remarkable feat, provided such proof holds scrutiny, of course…

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