The Fibonacci numbers are 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 253, ...
(And who doesn't love these fabulous numbers!)
Pretty much anything you want to know about these numbers can be found on Ron Knott's website. I especially like the connection to pinecones!
There are also many fabulous mathematical properties of the Fibonacci numbers. For example, here is an activity to explore some interesting divisibility properties of the Fibonacci numbers.