THE PUZZLET PAGE


PUZZLET 143

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.

Table

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


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