Certainly! Below is the test case generator for the given problem "Symmetric Ternary."

```python
import random

def generate_test_case():
    w = random.randint(1, 100000)
    return w

# Example usage:
if __name__ == "__main__":
    test_cases = [generate_test_case() for _ in range(10)]
    for test_case in test_cases:
        print(test_case)
```

This `generate_test_case` function generates a single random integer `w` in the range from 1 to 100,000, as specified in the problem statement. You can call this function multiple times to generate multiple test cases.

### Explanation

1. **Range of `w`**: The weight `w` is randomly chosen from 1 to 100,000.
2. **Output**: Each test case is a single integer `w`.

You can run this script to generate multiple test cases for the problem. Here's how you might call it to generate 10 test cases:

```python
if __name__ == "__main__":
    test_cases = [generate_test_case() for _ in range(10)]
    for test_case in test_cases:
        print(test_case)
```

This will print 10 random test cases, each being a single integer in the range [1, 100000]. You can adjust the number of test cases generated by changing the range in the list comprehension.