Building on the other answers, I wanted to share an example of using the while loop construct to achieve a do-while behaviour. By using a simple boolean variable in the while condition (initialized to TRUE), and then checking our actual condition later in the if statement. One could also use a break keyword instead of the continue <- FALSE inside the if statement (probably more efficient).
df <- data.frame(X=c(), R=c())
x <- x0
continue <- TRUE
while(continue)
{
xi <- (11 * x) %% 16
df <- rbind(df, data.frame(X=x, R=xi))
x <- xi
if(xi == x0)
{
continue <- FALSE
}
}