------
## 最终结论
```python
def odd_bit_set_number(n):
    # Create a mask with all odd bits set to 1
    mask = 0b10101010101010101010101010101010  # This is a 32-bit mask
    return n | mask

# Test cases
assert odd_bit_set_number(10) == 15
assert odd_bit_set_number(20) == 21
assert odd_bit_set_number(30) == 31
```