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 type 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 and 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 give a Smith number which was larger
than the telephone number of his brother-in-law. It is your task to find
Smith numbers which are larger than 4937775.
The input consists of several test cases, the number of which you are given in
the first line of the input.
Each test case consists of one line containing a
single positive integer smaller than 109.
For every input value n, you are to
compute the smallest Smith number which is larger than n
and print each number on a single line. You can assume
that such a number exists.
1
4937774
4937775
Miguel Revilla
2000-11-19
