A Self-Generating Sequence

A
series is formed from any integer n(0) as follows. The sum of the
digits of n(0) is s(0). n(1) = n(0) + s(0). If n(1)
is exactly
divisible by s(1), the series is terminated. If it's not, n(2) = n(1) +
s(0), and so forth. |

Example: take the series starting with 23.
giving 23, 28, 38, 49, 62, and 70. Since 70 is divisible by the
sum of its digits, 7, the series terminates and thus contains six terms. |

What is the greatest number of terms in any
series whose first term is less than 1,000? |

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Last Updated: February 4th, 2010.