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Shiny Numbers (Posted on 2013-06-20) Difficulty: 3 of 5
A positive integer is called shiny if it can be written as the sum of two not necessarily distinct integers a and b which have the same sum of their digits. For instance, 2012 is shiny, because 2012 = 2005 + 7, and both 2005 and 7 have the same sum of their digits. Find all positive integers which are not shiny (the dark integers).

No Solution Yet Submitted by Danish Ahmed Khan    
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Question Why?...a formal proof is a challenge | Comment 3 of 6 |
Smallest number whose sum of digits is 2n+1,  n=0.1,2...

It might be interesting to prove this feature of being "dark".
Apparently Sloane is not aware of it.

  Posted by Ady TZIDON on 2013-06-21 04:37:31
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