What are Happy Numbers?



 

They don’t smile when you say cheese. They don’t laugh at your jokes. And certainly, they don’t strike wacky poses. But one thing for sure, you will smile once you hear their name… For they are the HAPPY NUMBERS!

Mathematics and the world of physical sciences have called weird names to some things with unique properties. Perfect numbers had been previously featured. Now it’s the turn for happy numbers… So what are happy numbers? What makes them happy?

A number is considered as happy when it satisfies the following process:


  • Starting with any positive integer, replace the number by the SUM of the SQUARES of its digits.
  • Repeat the process until the number equals 1 (where it will stay), or it loops endlessly in a cycle which does not include 1.


Get it? Or still confused? To understand it better, let’s have an example, say 7. Now, its associated sequence of squares and sums is:

72 = 49
42 + 92 = 97
92 + 72 = 130
12 + 32 + 02 = 10
12 + 02 = 1

Voila! That’s it! Such a happy and lucky 7! Let’s consider another example, 566.

52 + 62 + 62 = 97
92 + 72 = 130
12 + 32 + 02 = 10
12 + 02 = 1

The first ten happy numbers (or should I say happiest? LOL) are: 1, 7, 10, 13, 19, 23, 28, 31, 32, and 44.





So if those numbers for which the iteration process ends in 1 are called as happy numbers, what do we call those which do not end in 1? Well, just the opposite – they are the UNHAPPY or SAD numbers.

There is no clear history of the happy numbers. I just suppose they are called happy because they end up in 1. Who would not like to be the first and the only one? :D

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