Time Limit: 2 Seconds
Memory Limit: 65536 KB
While skimming his phone directory in 1982, Albert Wilansky, a mathematician
of Lehigh University, noticed that the telephone number of his brother-in-law
H. Smith had the following peculiar property: The sum of the digits of that
number was equal to the sum of the digits of the prime factors of that number.
Got it? Smith��s telephone number was 493-7775. This number can be written as
the product of its prime factors in the following way:
The sum of all digits of the telephone number is 4+9+3+7+7+7+5=
42� , and the sum of the digits of its prime factors is equally 3+5+5+6+5+8+3+7=
42. Wilansky was so amazed by his discovery that he named this kind of numbers
after his brother-in-law: Smith numbers.
As this observation is also true for every prime number, Wilansky decided later
that a (simple and unsophisticated) prime number is not worth being a Smith
number, so he excluded them from the definition.
Wilansky published an article about Smith numbers in the Two Year College Mathematics
Journal and was able to present a whole collection of different Smith numbers:
For example, 9985 is a Smith number and so is 6036. However,Wilansky was not
able to find a Smith number that was larger than the telephone number of his
brother-in-law. It is your task to find Smith numbers that are larger than 4937775!
The input consists of a sequence of positive integers, one integer per
line. Each integer will have at most 8 digits. The input is terminated by a
line containing the number 0.
For every number n > 0 in the input, you are to compute the smallest Smith
number which is larger than n, and print it on a line by itself. You can assume
that such a number exists.
Source: Mid-Central European Regional Contest 2000