G - Self Numbers(2.2.1)

Description

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

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 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.

Input

No input for this problem.

Output

Write a program to output all positive self-numbers less than 10000 in increasing order, one per line.

Sample Output

135792031425364 | |       <-- a lot more numbers |9903991499259927993899499960997199829993

#include <iostream>#include <cmath>using namespace std;int main(){    int i , n , sum ;    int a[10001] ;    for(i=1;i<=10000;i++)        a[i] = i ;    for( i = 1 ; i <= 10000 ; i++ )    {        n = i ;        sum = n ;        while( n != 0 )        {            sum += n % 10 ;            n /= 10 ;        }        //cout<<sum<<endl;        if( a[sum] == sum && sum <= 10000 )            a[sum] = -1 ;    }    for(i=1;i<=10000;i++)        if( a[i] == i )            cout<<a[i]<<endl;    return 0;}