: Mathématiques: happy number

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happy number

In number theory, a happy number is a number which eventually reaches 1 when replaced by the sum of the square of each digit. For instance, 13 is a happy number because ${\\displaystyle 1^{2}+3^{2}=10}$ , and ${\\displaystyle 1^{2}+0^{2}=1}$ . On the other hand, 4 is not a happy number because the sequence starting with ${\\displaystyle 4^{2}=16}$ and ${\\displaystyle 1^{2}+6^{2}=37}$ eventually reaches ${\\displaystyle 2^{2}+0^{2}=4}$ , the number that started the sequence, and so the process continues in an infinite cycle without ever reaching 1. A number which is not happy is called sad or unhappy.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Happy_number)