Trying to simulate Poisson samples using inverse CDF method but my R function produces wrong results

I wrote some R code for simulating random samples from a Poisson distribution, based on the description of an algorithm (see attached image). But my code does not seem to work correctly, because the generated random samples are of a different pattern compared with those generated by R's built-in rpois() function. Can anybody tell me what I did wrong and how to fix my function?

r.poisson <- function(n, l=0.5)
{
  U <- runif(n)
  X <- rep(0,n)
  p=exp(-l)
  F=p
  for(i in 1:n)
  {
    if(U[i] < F)
    {
      X[i] <- i
    } else
    {
      p=p*l/(i+1)
      F=F+p
      i=i+1
    }
  }
  return(X)
}

r.poisson(50)

The output is very different from rpois(50, lambda = 0.5). The algorithm I followed is: