# Articles by Neonira

### Collatz Sequence – part 6

June 17, 2018 |

Proof of Collatz sequence convergence.

### Collatz Sequence – part 5

June 15, 2018 |

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...]

### Collatz Sequence – part 4

June 6, 2018 |

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...]

### Collatz Sequence – part 3

June 5, 2018 |

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...]

### Collatz Sequence – part 2

June 2, 2018 |

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 ...