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PUZZLET 168

An Integer's Digits Cubed Revisited

A sequence is formed when each term is the sum of the cubes of its predecessor. For example, if the first term is abc, the second term will be a^3 + b^3 + c^3. The third term will then be formed from the second term in the same manner.

Eventually, one of the terms will be the same as an earlier term, and the sequence will then loop around between the two terms forever.

What is the longest loop length for any sequence starting below 15,000?



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Last Updated: January 16th, 2010.