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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Prakhar Gupta: 2013-10-27 07:31:38

@abdelkarim, pls check my sol 10357831, i dont know why i m getting WA

Ouditchya Sinha: 2013-09-15 15:24:50

There is a case which one can tend to overlook!! Too easy though. ;) :)

numerix: 2013-09-15 08:09:57

@Arman Singh: Source limitation is self-explaning for that kind of problem.

mystique_blue: 2013-09-15 07:12:46

After this People may try HARSHAD.

mystique_blue: 2013-09-15 07:12:09

Its not challenge type then why the limit on size?
@numerix : iwas saying that the limit could hhave been..say..5000, no one will be able to put the answer (what you meant by self explaining) in those many chars ;)

Last edit: 2013-09-15 14:50:04

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