/*

  Euler problem 45
  """
  Triangle, pentagonal, and hexagonal numbers are generated by the following formulae:
 
  Triangle 	  	Tn=n(n+1)/2 	  	1, 3, 6, 10, 15, ...
  Pentagonal 	  	Pn=n(3n−1)/2 	  	1, 5, 12, 22, 35, ...
  Hexagonal 	  	Hn=n(2n−1) 	  	1, 6, 15, 28, 45, ...
  
  It can be verified that T(285) = P(165) = H(143) = 40755.
  
  Find the next triangle number that is also pentagonal and hexagonal.
  """ 

  This Pop-11 program was created by Hakan Kjellerstrand (hakank@gmail.com).
  See also my Pop-11 / Poplog page: http://www.hakank.org/poplog/

*/

compile('/home/hakank/Poplib/init.p');

define pent(n);
    n*(3*n-1)/2;
enddefine;

define tri(n);
    n*(n+1)/2;
enddefine;

define hex(n);
    n*(2*n-1);
enddefine;


define problem45;

    lvars t = 285+1;
    lvars tt = tri(t);
    lvars p = 165;
    lvars pp = pent(p);
    lvars h = 143;
    lvars hh = hex(h); 
    
    while true do
        if tt = pp and pp = hh then quitloop endif;

        t+1->t;
        tri(t)->tt;
        if tt > pp then  p+1->p; pent(p)->pp; endif;
        if pp > hh then  h+1->h; hex(h)->hh; endif;
        if tt > hh then  h+1->h; hex(h)->hh; endif;
    endwhile;

    ;;; [t ^t tt ^tt p ^p pp ^pp h ^h hh ^hh]=>
    tt=>
enddefine;


'problem45()'=>
problem45();