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PUZZLET 145

Self-Generating Sequences Revisited

From any integer n(0) form n(1) by multiplying the number of digits by each digit's value like this.

129 makes:  3 (nr of digits) x 1 x 2 x 9 = 54.

Now form n(2) from n(1) in the same way, etc. Eventually, two successive terms will be the same, or one of the terms in the sequence is repeated somewhere else in the sequence, at which point the sequence terminates.

What is the greatest length sequence that can be formed from a 3-digit integer?



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Last Updated: January 14th, 2010.