Hi, Coding problem

  Hi, there 

 

  Below is my code to one Homework question. I couldn't come up with the reasonable answer. 

    could you please help me to figure out what is the problem with my code? 
    thank you 


    Question is Coding P{X=j} =(1/2)^(j+1) + (1/2) *2^(j-1)/3^j
    my code is 
    sim <- function(n.gen){
    urandom <- runif(n.gen)
    sim.vector <- rep(0,n.gen)
    for(j in 1:n.gen){
     i <- 1
     p <- 5/12
     F <- p
     while(urandom[j] >= F){
      p <- p*((1/2)^(i+1)+1/3*(2/3)^i)/((1/2)^i+(1/2)*(2/3)^i)
      F <- F+p
      i<-i+1
      }
     sim.vector[j] <- i
    }
    # output
    sim.vector
    }
    
     
    
    result is 
    
       1    2    3    4    5    6    7    8   11 
    0.37 0.22 0.16 0.13 0.05 0.02 0.03 0.01 0.01 
    
     
    
    always, there are some numbers missing, it should be continuous. 
    
    why 9 and 10 are missing 
    
    thank you 
    
    
    
    sophia