Juicy questions 1: Six digit numbers and the question of patterns

I have a small number of questions that pop into my head from time to time. I bat them away because they're juicy and I'd like to consider them another time. I never do though. Until now though. My question, which I think I've been thinking about since I was a child, is this:

How many numbers have patterns in them?

Let's restrict it to 6 digit numbers for sake of example. My phone number used to be like this (digits have been substituted): 230191. That 191 is a pattern, as the digit 1 is repeated either side of the 9. 

I'm using one time codes in lots of places now. A lot of the time* the third and fourth numbers seem to be the same. That feels like a pattern too. As does 128348, and so on.

The key question then is, "what is a pattern?". Apart from repeated digits, can we generalise it? That is why it's a juicy question, and I'd welcome any wisdom on it.

*This is one of those hundred or so cognitive biases.