# Number Gossip

(Enter a number and I'll tell you everything you wanted to know about it but were afraid to ask.)

## Rare Properties of 429

The n-th *Catalan* number is equal to (2n choose n)/(n+1) = (2n)!/(n!(n+1)!).

There are many ways Catalan numbers can be interpreted; there are some cool pictures here and the Wikipedia article is very good.

## Common Properties of 429

To build the *lucky* number sequence, start with natural numbers. Delete every second number, leaving 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, ... . The second number remaining is 3, so delete every third number, leaving 1, 3, 7, 9, 13, 15, 19, 21, ... . The next number remaining is 7, so delete every 7th number, leaving 1, 3, 7, 9, 13, 15, 21, ... . The next number remaining is 9, so delete every ninth number, etc.

Those numbers were lucky they weren't crossed out.