The Luhn formula is a simple checksum formula used for validating identification numbers. It is designed to protect against accidental errors in data entry but not malicious attacks. For example, on a website a user may enter a credit card number or ISBN and sometimes these numbers may be mistyped. One can then use the Luhn formula to determine if the entered number is a valid one.

The validation algorithm is as follows:

  1. From the rightmost digit, double the value of every other digit.
  2. If a doubled value has two digits then add the digits individually.
  3. The number is valid under the Luhn formula: if the sum of all the digits is divisible by 10 (sum mod 10 == 0)

For Example, consider the number 1762483. We want to determine if it is a valid identification number using the Luhn formula?

Number | 1 | 7 | 6 | 2 | 4 | 8 | 3 Double every other digit |1 | 14 | 6 | 4 | 4 | 16 | 3 Sum digit | 1 | 5 | 6 | 4 | 4 | 7 | 3

Total Sum = 1 + 5 + 6 + 4 + 4 + 7 + 3 = 30

The total sum (30) is divisible by 10 and hence 1762483 is valid under the Luhn formula.

Here is the actual implementation in python

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def luhn_formula_validator(input):
	'''Check the input number under the Luhn Formula

	Parameters:
	-----------
	input: input number as sting.

	Returns:
	--------
	boolean
	'''

	#convert digits to list
	input_list = [int(x) for x in input]

	position = 1
	sum = 0
	for number in input_list:
		if position % 2 == 0:
			number = number * 2

		#sum individual digits of a doubled digit
		if number > 9:
			number = 1 + number % 10

		sum += number
		position += 1

	return sum % 10 == 0