You can use podcasting or slidecasting as a way to create and share patterns.

Use random.org or similar to generate a list of at least 20 random numbers, use one number per slide and create a presentation, be creative! Add music and upload the results to youtube or vimeo or slideshare. You can do the same for any number pattern, share results and see if other pupils can find the nth term.
Here’s a fun one

But you might like to start with something much more simple such as this then challenge your class to do better!