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).

(In reply to Why?...a formal proof is a challenge by Ady TZIDON)

In the opening comment I always had in my mind something about proof.  Admittedly I made "random" selection of numbers (those weren't the only ones by the way) but I was leaving open the thought that something might appear that I hadn't considered.  Then too was the D3 rating, that troubled me with my small find.

Charlie has seemingly filled those gaps. 

If you can't find something related with Neil Sloane then maybe Charlie could provide him with his dissertation. 

As an aside, I note from time to time that people offer "descriptive" numbers for us to find.  One I recall from outside Perplexus was "happy" numbers.

Is there a 'compendium' somewhere which defines such oddities? 
Or do some people ascribe their own definition to a given property?

Posted by brianjn on 2013-06-21 05:03:37