#|
  Euler #45 in Racket

  """
  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 Racket program was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Racket page: http://www.hakank.org/racket/

|#

#lang racket

(provide (all-defined-out))

(require (only-in math/number-theory
                  triangle-number pentagonal-number hexagonal-number
                  ))
;;; (require racket/trace)

(require (only-in "utils_hakank.rkt"
                  time-function
                  ))

;;; cpu time: 359 real time: 360 gc time: 6
(define (euler45a)
  (let* ([t 286]
         [tt (triangle-number t)]
         [p 165]
         [pp (pentagonal-number p)]
         [h 143]
         [hh (hexagonal-number h)])
    (for ([_ (in-naturals)]) ;;; It's annoying that this is needed. How to fix it?
          #:break (and (= tt pp)
                       (= pp hh))
          (set! t (add1 t))
          (set! tt (triangle-number t))
          (when (> tt pp)
            (set! p (add1 p))
            (set! pp (pentagonal-number p)))
          (when (> pp hh)
            (set! h (add1 h))
            (set! hh (hexagonal-number h)))
          (when (> tt hh)
            (set! h (add1 h))
            (set! hh (hexagonal-number h)))
          )
    tt)
  )

(define (run) 
  (time-function euler45a)
  )

(run)