Happy number

Uncommon card · No. 184155

In number theory, a happy number is a number which eventually reaches 1 when the number is replaced by the sum of the square of each digit. For instance, 13 is a happy number because 12+32=10, and 12+02=1. On the other hand, 4 is not a happy number because the sequence starting with 42=16 and 12+62=37 eventually reaches 22+02=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. More generally, a b-happy number is a natural number in a given number base b that eventually reaches 1 when iterated over the perfect digital invariant function for p=2. The origin of happy numbers is not clear. Happy numbers were brought to the attention of Reginald Allenby (a British author and senior lecturer in pure mathematics at Leeds University) by his daughter, who had learned of them at school. However, they "may have originated in Russia."

Read on Wikipedia · Image Cmglee, Zscout370 and MapGrid, CC BY-SA 4.0