The number formed when the integers 1, 2, 3 • • • 2021 are strung together in increasing order, 12345678•••20192021 is transformed into a new number through the following algorithm: The first digit is taken, doubled, then added to the second digit. This sum is then doubled, and added to the third digit. This value is doubled, and added to the fourth digit, until we use up all of the digits, and a new number is formed. We repeat this process on the new number, and then on the number that is formed from the new number, continuing until we reach a one digit number. Find this one digit number.
