This sequence will generate a happy sequence for any number n. Your number must be in the set of natural numbers N {0, 1, 2, 3, 4,...}. To get the next number in a happy sequence from a number n, add the squares of the digits in n. If the number reaches 1, it is said to be a happy number, else it is unhappy. Note that an unhappy number n>0 always eventually lands somewhere on the cycle 4, 16, 37, 58, 89, 145, 42, 20, 4... Can you prove this?
