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Nth Newman–Shanks–Williams Prime

### Problem Statement  
The Newman–Shanks–Williams (NSW) prime numbers are a sequence of numbers defined recursively as follows:  

- `NSW(0) = 1`  
- `NSW(1) = 1`  
- `NSW(n) = 2 * NSW(n-1) + NSW(n-2)` for `n > 1`  

Write a function `newman_prime(n)` that computes the nth Newman–Shanks–Williams prime number.  

### Example Usage  
```python [main.nopy]
newman_prime(0)  # Output: 1
newman_prime(1)  # Output: 1
newman_prime(2)  # Output: 3
newman_prime(3)  # Output: 7
newman_prime(4)  # Output: 17
newman_prime(5)  # Output: 41
```
def newman_prime(n):
    """
    Calculate the nth Newman–Shanks–Williams prime number.

    Args:
        n (int): The index of the NSW prime number to compute.

    Returns:
        int: The nth NSW prime number.
    """
    # Base cases
    if n == 0:
        return 1
    if n == 1:
        return 1

    # Recursive case
    return 2 * newman_prime(n - 1) + newman_prime(n - 2)
Intermediate recursionmath
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