Self Numbers

In 1949 the Indian mathematician D.R. Kaprekar discovered a class of numbers called self-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 Kaprekar.) 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

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 has two generators, 91 and 100. A number with no generators is a self-number. There are thirteen self-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 self-numbers less than or equal 1000000 in increasing order, one per line.

Sample Output

1
3
5
7
9
20
31
42
53
64
 |
 |       <-- a lot more numbers
 |
9903
9914
9925
9927
9938
9949
9960
9971
9982
9993
 |
 |
 |

C Code

#include<stdio.h>
#include<math.h>
#define max 1000001

char a[max];

digit(int n)
{
	int sum=0;
	while(n)
	 {
		 sum+=n%10;
		 n=n/10;
	 }
	 return sum;
}


 main()
 {

	 int i,d,k,c=0;
	 for(i=1;i<=max;i++) a[i]=1;
	 for(i=1;i<=max;)
	   {
		  k=i;
		  while(1)
		   {
		      d = digit(k)+k;
		      if(d>=max || !a[d]) break;
			   a[d]=0;
			  k=d;
		  }
	           for (i++; !a[i]; i++);  
                                 
	 }


	   for(i=1;i<max;i++)
	     if(a[i]) 
	      printf("%d\n",i);
	 	
			 
	   return 0;
 }