
Self Numbers 
Time Limit: 1000ms, Special Time Limit:2500ms, Memory Limit:32768KB 
Total submit users: 63, Accepted users: 62 
Problem 10020 :
No special judgement

Problem description 
In 1949 the Indian mathematician D.R. Kaprekar discovered a class of numbers called selfnumbers. 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 selfnumber. There are thirteen selfnumbers 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 selfnumbers less than 10000 in increasing order, one per line.

Sample Input 
no input 
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 
Problem Source 
MCU1998

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