Power washing is not going to make the new stone look like the old. You might want to reconsider whether you need the stones to match. It's not uncommon to see replacement stones that don't match the original. Particularly since you are new to the house, live with it for a year and see if it still bothers you.

And not to get too esoteric, but there is a concept derived from Buddhist teaching called wabi-sabi that is described in all sorts of ways, but can be summed up as nothing lasts, nothing is finished, and nothing is perfect. If this is your first house, adopting this philosophy could save you a lot of angst . . . and money.

There are different "types" of bluestone. Depending on where it came from and the minerals in it, it can vary from grey, to grey-blue, to greenish blue, to tannish grey. Specifically you can google "full color bluestone" and compare those colors to "blue select bluestone". But also, even if you have similar mineral content, the older aged/oxidized steps may never really match newer ones.

There are lots of different variations and power washing will not help you out. I would suggest having a local contractor or supplier help you match the original.

and.. my comment.. bluestone fades to a grayer color within months and more within years. It will start to look weathered quicker than you think..so may match over time..