How do i iterate functions until convergence in R?

I am looking to iterate until convergence but I am not sure how i should code it.

A simple similar example is something like

$X_0=5 , Y_0=3$

for $n=1,2..$

$P_n=X_{n-1}-Y_{n-1}$

$Y_n=3P_n$

$X_n=P_n+Y_n$

and end when it converges.

I have seen that for the repeat loop it loops indefinitely with an exit condition but I am unsure how i can word the iterations within R and how to word the exit condition for convergence. Any references or help would be appreciated.