A Happy Number is one where the repeated process of squaring and adding the digits eventually gives an answer of 1.
For example: 13
- $13->1^{2}+3^{2}=1+9=10$
- $10->1^{2}+0^{2}=1$
- $1->1^2=1$ ... and so on.
If a sequence like this reaches 1 it will stay there.
13 is a Happy Number!
However some numbers do not reach one. For example: 14
- $14->1^{2}+4^{2}=1+16=17$
- $17->1^{2}+7^{2}=1+49=50$
- $50->5^{2}+0^{2}=25$
- $25->2^{2}+5^{2}=4+25=29$
- $29->2^{2}+9^{2}=4+81=85$
- $85->8^{2}+5^{2}=64+25=89$
- $89->8^{2}+9^{2}=64+81=145$
- $145->1^{2}+4^{2}+5^{2}=1+16+25=42$
- $42->4^{2}+2^{2}=16+4=20$
- $20->2^{2}+0^{2}=4$
- $4->4^{2}=16$
- $16->1^{2}+6^{2}=1+36=37$
- $37->3^{2}+7^{2}=9+49=58$
- $58->5^{2}+8^{2}=25+64=89$
which we've seen before...
14 is an Unhappy Number.
This procedure is an example of a Number Chain
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