Self Numbers In Jay Language

Following was one of the pre-interview puzzles for a famous software company.

When a natural number n is given, d(n) is defined as the number n itself added to the sum of n's digits.

For example, d(91) = 9 + 1 + 91 = 101

Here, n is called d(n)'s generator. In the example above, 91 is 101's generator. Some numbers have more than one generator; 101 has as generators not only 91 but also 100. On the other hand, there are numbers that do not have any generators and such numbers are called self-numbers by an Indian mathematician, D. R. Kaprekar (http://en.wikipedia.org/wiki/D._R._Kaprekar).

For example, 1, 3, 5, 7, 9, 20, 31 are self-numbers.

What is the sum of all self-numbers that are 1 or more, and less than 5000?

---

   base10=:10&#.               
   base10 1 2 3                         
 123                                 

   inversed=:^:_1               
   digits=:base10 inversed               
   digits 123                         
 1 2 3                                 

   add=:+                            
   over=:/                            
   sum=:add over                  
   sum 123 1 2 3                         
 129                                 

   of=:@                             
   generate=: add sum of digits 
   generate 123                     
 129                                   

   foreach=:"0                       
   geneach=:generate foreach   
   geneach 123 456                
 129 471                              

   except=:-.                         
   1 2 3 4 except 2 4                       
 1 3                   

   lessthan=:>:@i.@<:             
   lessthan 10                       
 1 2 3 4 5 6 7 8 9                   

   selfnum=: except geneach     
   sum of selfnum lessthan 5000
 1227365                              

Indented is what I typed in and unindented is the interpreter result.

The script above is an extended verbose version of what I actually stepped through when solving the puzzle for the first time. My original steps were close to the following:

   d=:10&#.^:_1
   g=:(+ +/@d)"0
   +/ (-. g) >:i.<:5000

I solved this puzzle with these steps in about 30 seconds(with runtime being about 0.1 sec) thanks to JayLanguage. Of course, the time spent in reading(and thinking simultaneously) the problem was not included in this short time. ;-)

--JuneKim