### Collatz Sequence – part 6

Proof of Collatz sequence convergence.

[Read more...] Proof of Collatz sequence convergence.

[Read more...]Find previous posts if you haven’t yet read them. first post, second post, third post, and fourth post.
Numerical approach for number made of 1 unique digit
First important result
All the numbers from 1 to 9, provides 1 as final output of Collatz ... [Read more...]

Find previous posts if you haven’t yet read them. first post, second post, third post, .
Analysis of cluster 1
A reminder first.
cluster 1 is made of numbers with unit digit being part of set S1 = { , , , }.
cluster 1 paths
Reusing results from second post about digit mutation, we can determine all the ... [Read more...]

On first post and second post parts, I set-up the mathematical context to prove Collatz conjecture.
Cluster analysis
To prove Collatz sequence conjecture, we need some extraneous analysis. Reusing results of digit mutation proof, we know that the transition path from one number to another is driven by its unit ... [Read more...]

On first post part , we got some intuition about Collatz sequence], that seems to be unproven yet. Let’s try to prove it mathematically.
Some mathematic reminders
Canonical form a a natural integer
We name canonical form any natural integer n, written under one of following forms
n = 10 t + u
...

[Read more...] Collatz sequence is a well known suite mathematical suite, remaining unproved as far as I know.
Let’s play with it and discover some of its secrets.
To discover its behavior, we stop whenever we reach 1 as input, otherwise depending on parity of υ...

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