A Sequence of Integer Digit Sums

An integer is divided by the sum of its own
digits. If there is no remainder, the result forms the next term. This
second term is also divided by the sum of its own digits. Once again,
if no remainder exists, the result forms the next term. This continues
until either a remainder exists or the next term is a single digit. Example: 1944, 108, 12, 4. This is considered to be a terminating 3-term sequence. If a sequence can't reach a single digit, it's non-terminating. What is the smallest integer that yields a terminating 2-term sequence? 3 terms? And 4 terms? |

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Last Updated: January 16th, 2010.