Bored people have been known to do funny things. Some such funny things are documented in the Online Encyclopedia of Integer Sequences, which I highly recommend checking out if you have a moment. To search the database, just type in a sequence, and press enter. Then, be amazed that your "random" sequence already has a name!

One such silly sequence is the one composed entirely of happy numbers. Happy numbers are numbers whose values eventually reduce to 1 when you repeatedly sum the squares of each digit in the number. For example, 7 is a happy number:

7 -->
7**2 = 49 -->
(4**2) + (9**2) = 97 -->
(9**2) + (7**2) = 130 -->
(1**2) + (3**2) + (0**2) = 10 -->
(1**2) + (0**2) = 1

Numbers that aren't happy are sad numbers. For example, 6 is a sad number:

6 -->
(6**2) = 36 -->
(3**2) + (6**2) = 45 -->
(4**2) + (5**2) = 41 -->
(4**2) + (1**2)  = 17 -->
(1**2) + (7**2) = 50 -->
(5**2) + (0**2) = 25 -->
(2**2) + (5**2) = 29 -->
(2**2) + (9**2) = 85 -->
(8**2) + (5**2) = 89 -->
(8**2) + (9**2) = 145 -->
(1**2) + (4**2) + (5**2) = 42 -->
(4**2) + (2**2) = 20 -->
(2**2) + (0**2) = 4 -->
(4**2) = 16 -->
(1**2) + (6**2) = 37 -->
(3**2) + (7**2) = 58 -->
(5**2) + (8**2) = 89

Once the sequence reaches 89, it gets stuck in a cycle of 89, 145, 42, 20, 4, 16, 37, 58, 89 that loops forever. Thus, it can never reach 1, and it can never be happy.

But it doesn't stop there. It turns out that people have spent time searching for happy numbers in other bases as well. Happy bases are those in which every number is happy. For the first 500 million numbers, only base 2 and base 4 are happy.

And... that's all I have for you. I know it's ridiculous, but it's a little bit fascinating too. How bored were the people who defined and/or calculated the happy numbers?