Ken's POTW

Productive Numbers, and a Series
Some smaller puzzles this time:
  1. Find all numbers i, such that i is equal to the sum of the squares of its digits.
  2. 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.
  3. The following series eventually repeats. Where?
    1, 11, 21, 1112, 3112, ...

Source: Original and previous puzzle experience.

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