# Happy numbers

Doctor Who, teaches Martha Jones about happy numbers when answering a quiz question about a sequence of happy prime numbers. (numbers which are both happy and prime). He momentarily criticizes her and other humans present for their lack of understanding, and expresses concern that schools no longer teach recreational mathematics.
Dr. Who (tenth)

Happy numbers are determined with a sequence of operations.

Take a number, separate it into its individual digits, square each digit, add the results. Continue until you reach a conclusion of one. Which makes it a happy number. However, if the process repeats itself, then it is not a happy number.

Symbolically

n1 n2 n3 → n12 + n22 + n32

Specific example

94

94 → 92 + 42→ 81 + 16 = 97

97 → 92 + 72 → 81 + 49 = 130

130 → 12 + 32 + 02 → 1 + 9 + 0 = 10

10 → 12 + 02 → 1 + 0 = 1

∴ 94 is a Happy ☺ number!

## Focus questions

• Are all numbers happy?
• What makes a number happy?
• What makes a number unhappy?
• Are all numbers happy or unhappy?

## Source

Happy Numbers: A platform for conjecture and Exploration. by James A Gerald & David Jay Hebert. Mathematics Teacher: Learning & Teaching PK-12. August 8, 2023.

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