/* 

  Harshad numbers in Picat.

  http://en.wikipedia.org/wiki/Harshad_number
  """
  A Harshad number, or Niven number in a given number base, is an integer that is 
  divisible by the sum of its digits when written in that base. Harshad numbers were 
  defined by D. R. Kaprekar, a mathematician from India. The word "Harshad" comes 
  from the Sanskrit harṣa (joy) + da (give), meaning joy-giver. The Niven numbers 
  take their name from Ivan M. Niven from a paper delivered at a conference on 
  number theory in 1977. All integers between zero and n are Harshad numbers 
  in base n.
  """

  Also see: http://oeis.org/A005349
  1,2,3,4,5,6,7,8,9,10,12,18,20,21,24,27,30,36,40,42,45,48,50,54,60,63,70,72,80,81,84,90,100,102,108,110,111,112,114,117,120,126,132,133,135,140,144,150,152,153,156,162,171,180,190,192,195,198,200,201,204

  This Picat model was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/


% import util.
import cp.


main => go.


go =>
     Limit = 10000,
     Base = 10,
     X :: 1..Limit,
     IntLen = int_len(Limit,Base),
     List = new_list(IntLen+1),
     List :: 0..Base-1,

     to_num(List, Base, X),
     X mod sum(List) #= 0,

     % Vars = List ++ [X],
     All=solve_all(X),

     writeln(all=All),
     % writeln(list=List),
     nl.

% check if N is a Harshad number
harshad(N, Base) => 

     IntLen = int_len(N,Base),
     List = new_list(IntLen+1),
     List :: 0..Base-1,

     X #= N,
     to_num(List, Base, X),
     X mod sum(List) #= 0,

     Vars = List ++ [X],
     solve(Vars).



%
% converts a number Num to/from a list of integer List given a base Base
%
to_num(List, Base, Num) =>
   Len = length(List),
   Num #= sum([List[I]*Base**(Len-I) : I in 1..Len]).


int_len(V,Base) = Len =>
  Len1=1,
  while (V > Base-1)
     Len1 := Len1 + 1,
     V := V div Base
  end,
  Len = Len1.