Proof of Collatz sequence convergence. Some reminders first Remember Collatz sequence definition Let’s divide the Collatz sequence into two independent suites, for analysis convenience. First suite ω is for numbers: ωn + 1 = 3 ωn + 1 Second suite η is for numbers: ηn + 1 = ηn / 2 Resolution for numbers from 2 to 11 resolution graph First, let’s proceed ...

Proof of Collatz sequence convergence.

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 ...

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...