Problem 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.

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

 

Sample Output

 

Source

Mid-Central USA 1998

尼玛，太简单了，之间就水过去了.....

代码：