BOB Number

Little Bob loves to play with numbers. Recently he came up with a new series of numbers. For any positive integer n, define d(n) to be n plus the sum of the digits of n. (The d stands for digitadition, a term coined by Bob.) For example, d(75) = 75 + 7 + 5 = 87. Given any positive integer n as a starting point, you can construct the infinite increasing sequence of integers n, d(n), d(d(n)), d(d(d(n))), …. For example, if you start with 33, the next number is 33 + 3 + 3 = 39, the next is 39 + 3 + 9 = 51, the next is 51 + 5 + 1 = 57, and so you generate the sequence

 

33, 39, 51, 57, 69, 84, 96, 111, 114, 120, 123, 129, 141…

 

The number n is called a generator of d(n). In the sequence above, 33 is a generator of 39, 39 is a generator of 51, 51 is a generator of 57, and so on. Some numbers have more than one generator: for example, 101 have two generators, 91 and 100. A number with no generators is a BOBnumber. There are thirteen BOB-numbers less than 100: 1, 3, 5, 7, 9, 20, 31, 42, 53, 64, 75, 86, and 97.

Write a program to output all positive BOB-numbers less than or equal 1000000 in increasing order, one per line.

 

using System;

using System.Collections.Generic;

using System.Linq;

using System.Text;

using System.Diagnostics;

 

namespace BobNumbers

{

    class Program

    {

        static void Main(string[] args)

        {

            Console.WriteLine("Printing Bob numbers less than or equal to 1000000");

            Stopwatch watch = new Stopwatch();

            watch.Start();

            int num = 1000000;

            int[] bobNumbers = new int[num];

            for (int i = 0; i < num; i++)

            {

                int j = i + 1;

                while (j != 0)

                {

                    int temp = DigitAddition(j);

                    if (temp <= num && bobNumbers[temp – 1] != 1)

                    {

                        bobNumbers[temp – 1] = 1;

                        j = temp;

                    }

                    else

                    {

                        j = 0;

                    }

                }

            }

            for (int i = 0; i < num; i++)

            {

                if (bobNumbers[i] != 1)

                {

                    Console.WriteLine((i + 1).ToString());

                }

            }

            watch.Stop();

            Console.WriteLine("Elapsed: {0}", watch.Elapsed);

        }

        public static int DigitAddition(int num)

        {

            string str = num.ToString();

            int sum = 0;

            for (int i = 0; i < str.Length; i++)

            {

                sum = sum + int.Parse(str[i].ToString());

            }

            return (num + sum);

        }

    }

}

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