Debit card luhn algorithm

The Luhn algorithm is a simple checksum formula used to validate various identification numbers, including credit card numbers and debit card numbers. It's designed to help verify that the number is valid and helps to catch common errors in typing.

Here’s how the Luhn algorithm works step by step:

1. **Starting from the right**, or the last digit, take each digit in the number. Assign a position to each digit, starting from 1 for the last digit (the check digit).

2. **Double every second digit** (the digits in the odd positions from the right). If doubling a digit results in a number greater than 9, subtract 9 from the result. 

3. **Sum all the digits**, both those that were doubled and those that were not.

4. **Check the total**:
   - If the total modulo 10 is 0 (i.e., the total ends in 0), then the number is valid according to the Luhn formula.
   - Otherwise, it is not valid.

### Example of the Luhn Algorithm

Let's validate the debit card number `4532 1486 7890 1234`.

1. Identify the digits:
   - 4 5 3 2 1 4 8 6 7 8 9 0 1 2 3 4

2. Starting from the right, double every second digit:
   - 4 (not doubled)
   - 5  →  6 (doubled)
   - 3 (not doubled)
   - 2  →  4 (doubled)
   - 1 (not doubled)
   - 4  →  8 (doubled)
   - 8 (not doubled)
   - 6  →  12 → 3 (doubled, subtract 9)
   - 7 (not doubled)
   - 8  →  16 → 7 (doubled, subtract 9)
   - 9 (not doubled)
   - 0  →  0 (doubled)
   - 1 (not doubled)
   - 2  →  4 (doubled)
   - 3 (not doubled)
   - 4  →  8 (doubled)

So the transformed sequence is:
- 4, 6, 3, 4, 1, 8, 8, 3, 7, 7, 9, 0, 1, 4, 3, 8

3. Add the results:
   - \(4 + 6 + 3 + 4 + 1 + 8 + 8 + 3 + 7 + 7 + 9 + 0 + 1 + 4 + 3 + 8 = 70\)

4. Check if the sum is valid:
   - \(70 \mod 10 = 0\)

Since the result is 0, the debit card number `4532 1486 7890 1234` is valid according to the Luhn algorithm.

### Implementation

You can implement this algorithm in various programming languages. Here is a simple example in Python:

```python
def luhn_check(card_number):
    digits = [int(d) for d in str(card_number)]
    check_sum = 0

    # Process digits from right to left
    for i in range(len(digits)):
        if (len(digits) - i) % 2 == 0:  # Double every second digit
            double = digits[i] * 2
            check_sum += (double - 9) if double > 9 else double
        else:
            check_sum += digits[i]

    return check_sum % 10 == 0

# Example usage
card_number = "4532148678901234"
is_valid = luhn_check(card_number)
print(f"The card number {card_number} is {'valid' if is_valid else 'invalid'}.")
```

This function checks a card number against the Luhn algorithm and returns whether it's valid or not.