257*3+ 13=784/2/2/2/2=49

49*3+ 13= 160/2/2/2/2/2=5

5*3+ 13=28/2/2=7

7*3+ 13=34/2= 17

17*3+ 13=64/2/2/2/2/2= 1

1*3+ 13= 16/2/2/2/2= 1

The following cycle is16->1

The result of (1) number 257 after 257 "h operations" is 8. Because 257 gets 1 after 22 H operation, 64 after 1 H operation, 32 after 2 H operation, 16 after 3 H operation and 16 after 4 H operation.

257-22=235

235=7*33+4, so the result of 257 "H operation" is 8.

(2) As far as the number 257 is concerned, it finally enters the cycle16->; 1, the result of "h operation" 2 is always a constant 1.

For other numbers, it is uncertain whether the constant 1 will always be obtained. Because if we can find a way to prove that the constant 1 will always be obtained for other numbers, then the famous 3n+ 1 problem (so-called koala's conjecture or corner-valley conjecture) should also be proved in this way. But in fact, the problem of 3n+ 1 has not found any clues to prove.