Finding a number based on how many loops of the Collatz Conjecture it takes to reach 1

Question

Basically, I want to write an algorithm to find out which number takes 500 iterations to reach 1. I tried some variations but couldn't get it right.

Here is my code so far:

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace sequence4
{
    class Program
    {
        static void Main(string[] args)
        {
            long startingNumber = 1;
            long count = 0;

            while (count != 500)
            {
                startingNumber = startingNumber * 2;
                count++;

                startingNumber = startingNumber / 3 - 1;
                count++;
            }
            Console.WriteLine(count);
            Console.WriteLine(startingNumber);
        }
    }
}

EDIT: Updated version of the code

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace sequence4
{
    class Program
    {
        static void Main(string[] args)
        {
            int number = 2;
            int count = 0;

            while (count != 500)
            {
                if (number % 2 == 0)
                {
                    number = 2 * number;
                    count++;
                }

                if (number % 2 != 0)
                {
                    number = (number / 3) - 1;
                    count++;
                }
            }
            Console.WriteLine(number);
            Console.WriteLine(count);
        }
    }
}

What is meant by this line `startingNumber = startingNumber / 3 - 1;`? — NASSER, Aug 19 '15 at 05:44
Just trying to apply the reverse logic for the Colltz Conjecture, but it's wrong. — Filipe Barreto Peixoto Teles, Aug 19 '15 at 05:46
@X-TECH No worries, I just really wanna know how to solve this = ) — Filipe Barreto Peixoto Teles, Aug 19 '15 at 07:08
I see a few separate problems, but the main one is that when running it in reverse, instead of which of the two operations to take always being forced, you usually have an option: you can *always* double the current number, and if the current number is one more than a multiple of 3, you *could* instead take that multiple. Think about this: 2^500 is obviously one number that takes 500 iterations to reach 1. — j_random_hacker, Aug 19 '15 at 11:27
@X-TECH: Do a few iterations. Or you can try 2^10 = 1024, which takes 10 iterations. — j_random_hacker, Aug 19 '15 at 12:11
@j_random_hacker But 7 takes 16 iteration to reach 1 and 2^16 != 7 — NASSER, Aug 19 '15 at 12:13

score 2 · Answer 1 · edited May 23 '17 at 12:22

Collatz Conjecture's example is:

Consider, we have a number 7 and we need to reach 1 using the Collatz Conjecture

7 is odd so we use the algorithm 3(7) + 1 = 22
22 is even so we use 22/2 = 11
11 is odd so we use the algorithm 3(11) + 1 = 34
34 is even so we use the algorithm 34/2 = 17
17 is odd so we use the algorithm 3(17) + 1 = 52
52 is even so we use the algorithm 52/2 = 26
26 is even so we use the algorithm 26/2 = 13
13 is odd so we use the algorithm 13(3) + 1 = 40
40 is even so we use the algorithm 40/2 = 20
20 is even so we use the algorithm 20/2 = 10
10 is even so we use the algorithm 10/2 = 5
5 is odd so we use the algorithm 5(3) + 1 = 16
16 is even so we use the algorithm 16/2 = 8
8 is even so we use the algorithm 8/2 = 4
4 is even so we use the algorithm 4/2 = 2
2 is even so we use the algorithm 2/2 = 1

For Odd Number: x = 3n + 1
For Even Number: x = n / 2

We have applied the algorithm 16 times for the number 7 and we got to 1. So, 16 is the cycle length.

Now, if we take above example, we need to move reverse from bottom line to 500 times upward. For reverse iterations, we use:

For Odd Number: x = (n - 1) / 3
For Even Number: x = n * 2

Now, programmatically, implement as:

using System;

namespace ConsoleApplication1
{
    class Program
    {
        static void Main(string[] args)
        {
            double output = 1;
            const int iterations = 500;
            for (var i = 1; i <= iterations; i++)
            {
                output = GetOutput(output);
                Console.WriteLine("Number after {0} iterations is: {1}", i, output);
            }
            Console.WriteLine("Required Number is: {0}", output);
            VerifyResult(output, iterations);
            Console.ReadKey();
        }

        private static double GetOutput(double input)
        {
            if (input == 1)
            {
                return 2;
            }
            var output = (input - 1) / 3;
            return output % 1 == 0 && output % 2 != 0 && output > 3 ? output : input * 2;
        }

        //To verify the above results we need this method
        private static void VerifyResult(double output, int iterations)
        {
            //-------------------------VERIFICATION-----------------------
            Console.WriteLine("Press any key to check iterations in reverse");
            Console.ReadKey();
            Console.WriteLine("Running validation process ...");
            var n = output;
            var max = n;
            var count = 0;
            Console.WriteLine("{0} (starting number in Collatz Sequence)", n);
            while (n > 1)
            {
                n = n % 2 == 0 ? n / 2 : 3 * n + 1;
                count++;
                if (n > max) max = n;
                Console.WriteLine(n);
            }
            if (count == iterations) //match here iterations and outputs
            {
                Console.WriteLine("\n\nCONGRATULATION! Verification results matched. :-)\n\n");
                Console.WriteLine("There are {0} cycle length in the sequence", count);
                Console.WriteLine("The largest number in the sequence is {0}", output);
                Console.WriteLine("\n\n-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-");
                Console.WriteLine("\n\nREQUIRED NUMBER: {0}\n\n", output);
                Console.WriteLine("-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-\n");
                Console.WriteLine("\nPress any key to exit");
            }
            else
            {
                Console.WriteLine("Oops... Verification results are not matching. :-(");
            }
        }
    }
}

Example's Source: Algorithm guidance with 3n+1 Conjecture

Finding a number based on how many loops of the Collatz Conjecture it takes to reach 1

1 Answers1