Here is a Python implementation of the described algorithm:

```python
import math

def sieve_of_eratosthenes(n):
    x = [True] * n
    x[0] = x[1] = False
    
    for j in range(2, math.isqrt(n) + 1):
        if x[j]:
            for k in range(j*j, n, j):
                x[k] = False
    
    prime_indices = [i for i in range(n) if x[i]]
    return prime_indices

# Input the value of n
n = 20
result = sieve_of_eratosthenes(n)

print("Prime numbers up to", n, "are at indices:", result)
```

You can run this code by copying and pasting it into a Python environment. Just change the value of `n` to the desired natural number for which you want to find prime indices. The code will output the indices of the array x that represent prime numbers according to the Sieve of Eratosthenes algorithm.