Happy Numbers
A happy number is one that ends in 1 when you follow this process:
For each number, separate it into its digits. For each digit, square the value, and add it together. Do this over and over again until you have a single digit. If the numbers end at 1, the number is 'happy'.
For example, 19 is happy, as the associated sequence is:
For each number, separate it into its digits. For each digit, square the value, and add it together. Do this over and over again until you have a single digit. If the numbers end at 1, the number is 'happy'.
For example, 19 is happy, as the associated sequence is:
On the other hand, 16 is NOT happy, (it is actually despairing) as the associated sequence is:
Challenge your students to find...
Discuss:
Fun Fact:
- The happy numbers from 1 to 100
Discuss:
- What patterns did you find?
- How can we decide if numbers are happy or despairing without doing all of the calculations?
- Can you find numbers that are BOTH happy and prime?
Fun Fact:
- "In the 2007 Doctor Who episode "42", a sequence of happy primes (313, 331, 367, 379) is used as a code for unlocking a sealed door on a spaceship about to collide with a star. When the Doctor learns that nobody on the spaceship besides himself has heard of happy numbers, he asks, "Don't they teach recreational mathematics anymore?"" Source: WIkipedia