Here's a Python code to implement the steps you've outlined. This algorithm resembles the Sieve of Eratosthenes, which is used to find all primes less than or equal to a given number n:

```python
import math

def sieve(n):
    # Step 1 & 2: Create an array x of boolean values initialized to True
    if n < 2:
        return []
    
    x = [True] * (n + 1)
    
    # Step 3: Set the first two positions (0 and 1) to False
    x[0], x[1] = False, False
    
    # Step 4: Start from the first prime number, 2
    limit = int(math.sqrt(n))
    for j in range(2, limit + 1):
        if x[j]:  # Step 4.1: Check if x[j] is still True
            # Update the multiples of j from j*j to n to False
            for multiple in range(j*j, n + 1, j):
                x[multiple] = False

    # Step 4.2: Find all indices that have the value True
    true_indices = [i for i, value in enumerate(x) if value]
    
    return true_indices

# Example usage
n = 30
result = sieve(n)
print(f"Indices with True values (primes up to {n}): {result}")
```

This script defines a function `sieve` which implements the sieve of Eratosthenes algorithm:
- It constructs a boolean array, marking non-prime numbers as `False`.
- The number 0 and 1 are not primes hence initially marked as `False`.
- For each number from 2 to the square root of `n` (rounded down), it marks its multiples as non-primes (`False`).
- Finally, it collects and returns the indices of the array which remain `True`, representing prime numbers.

You can test this function with different values of `n` to see the prime numbers up to `n`. The example provided sets `n` to 30 and prints the prime numbers up to 30.