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).

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.