Happy Numbers (Long)

A happy number is defined by the following Sequence: Starting with any positive integer, replace the number by the sum of the squares of its digits in base-ten, and repeat the process until the number either equals 1 (where it will stay), or it loops endlessly in a cycle that does not include 1. Those numbers for which this process ends in 1 are happy numbers, while those that do not end in 1 are sad numbers.

For example, 19 is happy, as the associated Sequence is:

1² + 9² = 82

8² + 2² = 68

6² + 8² = 100

1² + 0² + 0² = 1.

Print all the happy numbers from 1 to 1,000 inclusive, each on their own line.

Variants: Happy Numbers

External links: OEIS A007770, Rosetta Code, Wikipedia