The word 'exist' is doing a lot of work here. Could any computer actually find the value in pi? Each computation takes energy, and there is a finite amount of energy in the universe. Does the value 'exist' in pi if it could never be rendered? How much different is that claim from "our simulated universe is a file on gods computer, located just past the edge of the observable universe or 18 inches away in the 4th dimension"?
A similar thought experiment I've had is with the lottery. With just a few sheets of paper, there exist a sequence of numbers that would completely shut down both major US lotteries - ossibly even get you arrested - if they contained the winning numbers for the next 50, 20, or even 10 consecutive draws. Think about the consequences. You would win, and win again the next draw, and they would be certain you cheated. Then confiscate your pad, and draw again and win a third time. They would have to shut the contest down because this is "mathematically impossible ". But it's not. Just like your thought experiment, it's "just numbers"