Doctor Who mathematics

If you are fan of Doctor Who, then you might already know that the show regularly features mathematics...this clip is about Happy Primes...

What is a happy prime you ask?

You can think about a happy number in the following way. Take a positive integer, then replace the number by the sum of the squares of its digits. Take the new number, and repeat the process again and again. If the process eventually takes you to 1, then the original starting number is a happy number. If the process avoids 1 and goes into a cycle of numbers, then it is an unhappy number.

For example, 91 is happy, because it leads to the following sequence.

9² + 1² = 82
8² + 2² = 68
6² + 8² = 100
1² + 0² + 0² = 1 = happiness

Because 91 is prime, then it is not just a happy number, but also a happy prime.

If you are a Dr Who fan, you might like the BBC's Dr Who Fun and Games site.