MCUR98 - Self Numbers

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Background

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 ben 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.

Problem

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

Input

There is no input.

Output

All positive self-numbers less than 1000000 in increasing order, one per line.


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mag1x_: 2018-06-23 08:32:15

Easy oNe :)

karthik1997: 2017-12-12 09:14:47

250 bytes with DFS :P

Last edit: 2017-12-12 09:15:01
sandeep_4141: 2017-05-19 06:42:43

ideone gives me runtime error but spoj accept it ??

utkarsh538: 2016-04-13 22:54:59

simple naive solution :)

Siddharth Singh: 2016-01-05 17:05:53

Very Naive Solution Worked Surprisingly :D

dwij28: 2015-12-29 18:09:51

There are times when you want to break your own head. I feel the same at this moment. I did not read the word "less than 1000000" and sieved up to 1000000. Costed me 2 WA. Remember people 1000000 is "NOT" a self number. Beware of that. Sieve is your friend.

evil_hacker26: 2015-08-22 23:41:15

lolz...easy one....:p

:.Mohib.:: 2015-07-25 21:55:00

Very nice que...!!

.::Austin::.: 2015-01-14 22:21:55

Why the size limit???

Anubhav Balodhi : 2015-01-02 13:50:47

A classical mathematical question, ac ^_^


Added by:abdelkarim
Date:2013-09-15
Time limit:0.400s
Source limit:900B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:Mid-Central USA 1998