What number is a different random number every day?

I have a list containing the numbers between, say, 1 and 9. Now, I need an algorithm that randomly generates one of these numbers—but at any moment during the day it should produce the same number.

To clarify: let’s say that if I ran this algorithm this morning and it produced the number 3, then if my neighbour ran the same algorithm this evening, it should produce the number 3 as well. Likewise, if we had both ran it tomorrow, it should be likely to produce a different number than 3, but it should produce it twice.

It feels like a simple problem, but I can’t find a good answer…