To find the law of a natural number, do the following operations: if it is an even number, divide it by 2; if it is an odd number, add 1. Do this until 1, and the operation stops. Find out how many numbers become 1 after 8 operations?

There is one number that becomes one through one operation, that is, 2; there are two numbers that become one through two operations, that is, 4 and 1; there are two numbers that become one through three operations, that is, 3 and 8 After 6 operations, there are 8 numbers changed to 1, namely 11, 24, 10, 28, 13, 64, 31, 30; after 1, 2, 3, 4, 5 The number of operations changed to 1 is 1, 2, 3, 5, 8 The following numbers are: 5 + 8 = 13, 13 + 8 = 21, 21 + 13 = 34, that is to say, there are 34 numbers changed to 1 after 8 operations. A: there are 34 numbers changed to 1 after 8 operations

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