Sequence n.

The source is a mathematical proposition:

Write a natural number n at will and transform it according to the following rules:

If it is odd, the next step becomes 3N+ 1.

If it is an even number, the next step becomes N/2.

Not only students but also teachers, researchers, professors and pedants have joined in. Why is the charm of this game enduring? Because people find that no matter what number n is, it can't escape back to the bottom of 1. Accurately speaking, they can't escape the 4-2- 1 cycle that hit the bottom. You will never escape this fate. This is the famous "hail conjecture". For example, 9,28,14,7,22, 1 1 34,17,52,26,13,40,40.

The greatest charm of hail lies in its unpredictability. John conway, a professor at Cambridge University in England, discovered a natural number of 27. Although 27 is an unremarkable natural number, if calculated according to the above method, its fluctuation is extremely intense: first, 27 has to undergo 77 steps of transformation to reach the peak of 9232. Then it reaches the bottom value 1 through 32 steps. The whole transformation process (called hail process) needs11step, and its peak value is 9232, which is more than 342 times of the original number of 27. If compared with the waterfall-like straight-line falling (2 to the n power), it has the same hail course.

Do all positive integers conform to this law? Unfortunately, no one can prove this theory so far, so the hail conjecture is still an undiscovered treasure in the crown of mathematics.