# Exercise 3F-3

# Wondrous numbers

# Start with any positive integer n. Then each term is obtained from 
# the previous term as follows: if the previous term is even, the next 
# term is one half of the previous term. If the previous term is odd, 
# the next term is 3 times the previous term plus 1. No matter what 
# value of n, the sequence will always reach 1.

# Create wlengths to record the lengths of sequences

wlengths<-NULL

# Loop to generate the first 30 sequences

for (j in 1:30)
{
  
# Set input number to change this to change the sequence

wondrous<-j

  # No sequences are longer than 150. Start at 2 because we already have
  # the first term defined
  
  for (i in 2:150) 
  {
    
    # Break out of the loop if the last number is 1
    if (wondrous[length(wondrous)]==1) break
    
    # Calculate next term
    if (wondrous[i-1]%%2==0) 
    {
      # If even, next term is (last term)/2
      wondrous<-c(wondrous, wondrous[i-1]/2) 
    }
    else 
    {
      # If odd, next term is ((last term)*3)+1
      wondrous<-c(wondrous, (wondrous[i-1]*3)+1)
    }
  } # End of i loop

  # Create tempcounter to record the length of the sequence
  
  # Create a new loop to count the elements in wondrous
  for (k in seq(wondrous))
  {
    tempcounter<-k
  }

  # Add tempcounter to the end of wlengths

  wlengths<-c(wlengths,tempcounter)

  # Display sequence
  print(wondrous)
  
 } # End of j loop 

# Display wlengths to show the list of sequence lengths
wlengths