Right, but then they aren't random, right? I feel like this is a problem of semantics.. what do we mean by "random number"? I thought the definition was basically, "lack of pattern." What is a better definition?

In mathematical terms, random refers to a quantity which is "randomly" picked from a distribution. In a sense, things are only random in reference to a distribution.

A "random number" in the lay sense is a "random number from a uniform probability distribution"; a uniform distribution being one where each element is equally likely.

You might note there are still patterns in uniform distributions. e.g. Uniformly random integers are never not integers, and they also fit within a particular range: we have no way to pick random numbers uniformly between -infinity and infinity.

Well it's degrees of random. You just shift the probabilities. Rolling a die is still random even though you'll never roll a 7, or a 3.5, or a "b". Picking a number from a normal distribution is still random even though it's more likely to get you a sample from the center than from the edges.