Question

Within the 1900 folder on your desktop, create a new folder namned Lab4HwLastnameFirstnane (5 pts) Problem 1 Consider the sequence of integers defined as follows: • The first term is any positive integer. . For each term n in the sequence, the next tcrin is computed like this: If n is even the next term is n/2. If n is odd, the next term is 3n +1. • Stop once the sequence reaches 1. Here are a few examples of this sequence for different values of the first term: • 8, 4, 2, 1 • 12, 6, 3, 10, 5, 16, 8, 4, 2,1 • 19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1 Note that all throc of these eventually do reach 1. In fact, it is believed (but not known) that the sequence will always reach 1, regardless of the first term chosen. This is known as the Collatz conjecture. Despite its apparent simplicity, it has so far eluded all attempts at a proof. Mathematician Jeffrey Lagarias at the University of Michigan has claimed that this is an extraordinarily difficult problem, completely out of reach of present day mathematics." We might not be able to prove the Collata conjecture here, but we can experiment computationally with it within your Labdhw folder, write a program named Collatz, java that allows the user to enter any positive integer. The program should then compute and list all the ternis of the sequence until it reaches 1. At the end, show how many terms it took to get to 1 (including 1 itsell).

Answer 1

import java.util.Scanner;

public class Lab4HW {
   public static void main(String[] args) {
       Scanner sc = new Scanner(System.in);
       System.out.println("Enter starting value(must ne a positive integer): ");
       int n = sc.nextInt();
       int count = 1;
       // loop until n becomes 1
       while (n != 1) {
           count++;
           System.out.println(n);
           //if n is even dividing
           if (n % 2 == 0)
               n = n / 2;
           else
               // if n is odd adding 1 and multiply with 3
               n = 3 * n + 1;
       }
       System.out.println(n);
       System.out.println("Number of terms: " + count);
   }
}

Enter starting value(must 51 positive integer) ne a 16 2 1 Number of terms: 6

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