MCUR98 - Self Numbers
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.
hide comments
:.Mohib.::
2015-07-25 21:55:00
Very nice que...!! |
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.::Austin::.:
2015-01-14 22:21:55
Why the size limit??? |
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Anubhav Balodhi :
2015-01-02 13:50:47
A classical mathematical question, ac ^_^ |
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vsri293:
2015-01-01 18:32:31
cout gives tle..
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Sayak Haldar:
2014-12-30 20:56:17
dont use long long, takes additional time to print thus resulting tle |
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surayans tiwari(http://bit.ly/1EPzcpv):
2014-07-17 13:29:41
cakewalk.. make a seive and its done |
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Ankit Kumar:
2014-01-04 19:57:53
'less' than 1000000 not less than equal to 1000000
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(Tjandra Satria Gunawan)(曾毅昆):
2013-12-21 14:58:45
@numerix: awesome speed, all my best I/O in C/C++ can't beat your time record.. congratulations ;-) |
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Jumpy:
2013-12-21 11:50:20
sieves would be better....
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Vaibhav Gupta:
2013-10-28 16:51:12
strange...printf gives tle
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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 |