The function takes a string input and replaces every second letter (0-indexed) with a letter that comes two places after it in the alphabet, while keeping the numbers unchanged.

[CODE]: 
```python
def approximate_function(input_string):
    alphabet = "abcdefghijklmnopqrstuvwxyz"
    output_string = ""
    for idx, ch in enumerate(input_string):
        if ch.isalpha() and idx % 2 == 0:
            new_index = (alphabet.index(ch.lower()) + 2) % len(alphabet)
            if ch.isupper():
                output_string += alphabet[new_index].upper()
            else:
                output_string += alphabet[new_index]
        else:
            output_string += ch
    return output_string
```

Let's run the function on a few more inputs to verify the approximation.

COMMAND: PYTHON(./temp/function.py "Computational" "Algorithms" "Geeks" "exampleinput")