self-number.

 

 

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.

第一次写博客，好激动....不过这个题 纯暴力，从1开始到N，用打表的方法，从1开始找，找到就标记为1；然后就打出标记为0的数就行.不过，题意我读了好久，英语是硬伤，伤不起啊.... 从1开始，1+1=2，故2做上标记1；2+2=4；故4做上标记.......以此类推

#include <stdio.h>
int main()
{
    int i,cmp,w,prime[100005]= {0};
    for(i=1; i<=100000; i++)
    {
        cmp=w=i;
        while(w!=0)
        {
            cmp+=w%10;
            w/=10;
        }
        if(cmp<=100000)
            prime[cmp]=1;
    }
    for(i=1; i<=100000; i++)
        if(prime[i]==1)
            printf("%d\n",i);
    return 0;
}