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Problem 1006
Self Numbers
Time Limit: 1000ms
Memory Limit: 65536kb 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 10000 in increasing order, one per line. Input
Nothing
Output
Shown in sample output.
Sample 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 |