number-theoretic "games"

[Timothy Y. Chow]

Sara Uckelman wrote:

> Tonight at supper my partner introduced our 9yo to the Collatz 
> Conjecture.  She had so much fun with this "game" that it made me wonder 
> what other sorts of number theoretic results/conjectures/algorithms 
> would similarly be fun for a child who insists her favorite subject is 
> maths and hasn't yet been told that math isn't fun or isn't for girls.

This topic has come up on MathOverflow before.

https://mathoverflow.net/q/281447

> We've done the Sieve of Eratosthenes before, which was a hit, and prime 
> factorization, which wasn't.

You could try this game: Take a number x, reverse its digits to get 
another number y, and compute x+y.  Stop if x+y is palindromic, and 
otherwise, iterate.

https://en.wikipedia.org/wiki/Lychrel_number

Or how about this: have her compute 142857*n for n = 2, 3, 4, 5, 6, 7. 
Then experiment with 1/p for other primes p.  What happens if you compute 
1/81?

Tim