------
## 最终结论
```python
def power(x):
    steps = 0
    while x != 1:
        if x % 2 == 0:
            x //= 2
        else:
            x = 3 * x + 1
        steps += 1
    return steps

def get_kth_integer(lo, hi, k):
    power_values = {}
    for i in range(lo, hi + 1):
        power_values[i] = power(i)

    sorted_numbers = sorted(power_values.keys(), key=lambda x: (power_values[x], x))
    return sorted_numbers[k - 1]
```