Collatz Conjecture

Visualization

Odd and Even number

They both know the difference between odd and even number.

the conjecture

Use a_n = \frac{a_{n-1}}{2} to calculate the next number if a_{n-1} is an even integer, or use a_n = 3a_{n-1}+1 if a_{n-1} is an odd integer. Then from any positive interger a_0, for large engouth n, the sequence will always go into 1->4->2->1.

For example, 10->5->16->8->4->2->1, or longer version
9->28->14->7->22->11->34->17->52->26->13->40->20->10->5->16->8->4->2->1 have been demonstrated in the class.

Efforts until now

Computer have confirmed all the numbers smaller than 295 000 000 000 000 000 000 fulfill this conjecture.

Terence Tao (born in Shanghai, the world known genius) proved almost all numbers fulfill this conjecture in 2019.