Matt Parker: 145 and the Melancoil: Unhappy Numbers (アンハッピー数)

• Happification tree
• Unhappy numbers
• Melancoil numbers

Example:

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 -> 8^2 + 9^2 = 145

Ria Symonds: 7 and Happy Numbers (ハッピー数)

Example: 7

7
7^2 = 49
4^2 + 9^2 = 16 + 81 = 97
9^2 + 7^2 = 81 + 49 = 130
1^2 + 3^2 + 0^2 = 1 + 9 + 0 = 10
1^2 + 0^2 = 1 + 0 = 1

7 is a happy number


Example: 8

8
8^2 = 64
6^2 + 4^2 = 36 + 16 = 52
5^2 + 2^2 = 25 + 4 = 29
2^2 + 9^2 = 4 + 81 = 85
8^2 + 5^2 = 64 + 25 = 89
8^2 + 9^2 = 64 + 81 = 145
1^2 + 4^2 + 5^2 = 1 + 16 + 25 = 42
4^2 + 2^2 = 16 + 4 = 20
2^2 + 0^2 = 4 + 0 = 4
4^2 = 16
1^2 + 6^2 = 1 + 36 = 37
3^2 + 7^2 = 9 + 49 = 58
5^2 + 8^2 = 25 + 64 = 89

8 is not a happy number