15. For a positive integer, perform the following operations: if it is even, divide it by 2; if it is odd, add 1. Continue this process until you get 1 and stop. Then, the number of integers that become 1 after 10 operations is $\qquad$.

 untranslated part: $\qquad$ (This part is usually left for the answer to be filled in)
【Analysis】 55
Starting from 1 and working backwards, any number can be multiplied by 2 to get an even number, and the even number can be reduced by 1 to get an odd number; the first operation should be $1 \times 2=2$, with 1 number;
The second operation can be $2 \times 2=4$ or $2-1=1$, but 1 should be discarded, so there is only 1 number;
The third operation can be $4 \times 2=8$ or $4-1=3$, with 2 numbers;
Starting from the fourth operation, the numbers obtained should be the result of multiplying all the numbers from the previous operation by 2 and subtracting 1 from the even numbers, so the number of numbers obtained should be the number of numbers obtained from the previous operation (multiplying by 2 to get all the even numbers for this operation) and the number of numbers obtained from the operation before the previous one (only the even numbers obtained by multiplying all the numbers from the operation before the previous one by 2 can be reduced by 1 to get all the odd numbers for this operation);
Therefore, the number of numbers obtained from each operation are $1,1,2,3,5,8,13,21,34,55$;
Therefore, after 10 operations, there are 55 numbers that can become 1.