Explain neural networks with example which predict pattern

Neural networks are also called many other names. "Artificial intelligence" and "deep learning" are two names that I can come up with from the top of my head. It's actually very simply to explain in theory. Applying the principles are a lot tougher, however.

The simple of it is, in a large data set of any type, there are patterns. Human beings can make connections and deceiver many types of patterns. Neural networking is the artificial way to discover these patterns without human interference. Predictive pattern is also simple. If you have a series of numbers, 1, 3, 5,... I bet you could predict the rest of those numbers all the way to infinity because you very quickly recognize that this pattern is a list of all positive odd integers. Teach a computer to discover these same patterns and you've got a predictive pattern analysis.

for example if i randomly type numbers then neural network return me a set of number with look alike my pattern