```python
from typing import List

def window_max(readings: List[int], width: int) -> List[int]:
    if width < 1:
        raise ValueError("Width must be at least 1")
    
    max_values = []
    for i in range(len(readings) - width + 1):
        max_values.append(max(readings[i:i+width]))
    
    return max_values
```