## Ken's POTW

Productive Numbers, and a Series
Some smaller puzzles this time:
- Find all numbers
*i*, such that *i* is
equal to the sum of the squares of its digits.
- Find all numbers
*n*, such that *n* is
equal to the product of its
first three and last three digits (taken as 3-digit numbers).
Assume the first digit of *n* is not zero.
Ignore leading zeros in the second 3-digit number if necessary.
- The following series eventually repeats. Where?

1, 11, 21, 1112, 3112, ...

Source: Original and previous puzzle experience.

Solution

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