Oyster card checksum

Oyster card is a payment card issued by Transport for London for public transport within its network. Every Oyster card has a unique number on its back.

oyster card number

The number is in the format of 10 digits, followed by a checksum of 2 digits, both of which may include leading zeros, for example, 0000000000 00.

With some experiments, I found the checksum can be calculated with the following formula:

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def checksum(number: int) -> int:
    return (
        + number * 0x10
        + number // 0x1 * 3
        - number // 0x10 * 3
        + number // 0x100 * 3
        - number // 0x1000 * 3
        + number // 0x10000 * 3
        - number // 0x100000 * 3
        + number // 0x1000000 * 3
        - number // 0x10000000 * 3) % 100

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