Question

Why is this an impossible sequence to solve?
3x + 1 ?

thanks​

Answer 1

`T(x)=\begin{cases}(3x+1)/(2) & x\text{ is odd} \\ (x)/(2) & x\text{ is even}\end{cases} \\ for \: instance \: start \: with \: 7 \: \\ which \: is \: an \: odd \: number \\ (21 + 1)/(2) = (22)/(2) = 11 \\ 11 \: is \: odd \\ (11 + 1)/(2) = 6\\ 6 \: is \: even \\ (6)/(2) = 3 \\ 3\: is \: odd \\ (9 + 1)/(2) = 5 \: \\ 5 \: is \: odd\\ (15 + 1)/(2) = 8 \\ 8 \: is \: even \\ (8)/(2) = 4 \\ 4 \: is \: even \\ (4)/(2) = 2 \: then \: 1 \\`

Explanation:

Can we connect to 1 for all numbers?

A general proof for a simple pattern seems almost impossible, probably a new branch of mathematics maybe needed to tackle this conjecture...