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PUZZLET 199

A Sequence from Digit Sums & Products

A sequence is formed from integer n thus: if any of n's digits are zero,  n = n + the sum of its digits; if n contains no zeroes, n = the product of its digits. All subsequent terms are formed in the same way. The sequence terminates when a term is reduced to a single digit.

Example: 27, 41, 45, 65, 95, 140, 5.

For initial values under 1,000, find all sequences greater than 30 terms.



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Last Updated: January 19th, 2010.