Happy Number

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For example: 13

• $13->1^{2}+3^{2}=1+9=10$
• $10->1^{2}+0^{2}=1$
• $1->1^2=1$ ... and so on.

However some numbers do not reach one. For example: 14

• $14->1^{2}+4^{2}=1+16=17$
• $17->1^{2}+7^{2}=1+49=50$
• $50->5^{2}+0^{2}=25$
• $25->2^{2}+5^{2}=4+25=29$
• $29->2^{2}+9^{2}=4+81=85$
• $85->8^{2}+5^{2}=64+25=89$
• $89->8^{2}+9^{2}=64+81=145$
• $145->1^{2}+4^{2}+5^{2}=1+16+25=42$
• $42->4^{2}+2^{2}=16+4=20$
• $20->2^{2}+0^{2}=4$
• $4->4^{2}=16$
• $16->1^{2}+6^{2}=1+36=37$
• $37->3^{2}+7^{2}=9+49=58$
• $58->5^{2}+8^{2}=25+64=89$

14 is an Unhappy Number.

This procedure is an example of a Number Chain

• http://en.wikipedia.org/wiki/Happy_number
• http://mathworld.wolfram.com/HappyNumber.html