045.lisp

(defun isInteger (n)
  (= (round n) n))

(defun isPentagonalNumber (p)
  (let ((solution (/ (+ 1 (sqrt (+ 1 (* 24 p)))) 6)))
    (isInteger solution)))

(defun test (p)
  (/ (+ 1 (sqrt (+ 1 (* 24 p)))) 6))

(defun PentagonalNumber (n)
  (* n (/ (- (* 3 n) 1) 2)))

(defun isHexagonalNumber (h)
  (let ((solution (/ (+ 1 (sqrt (+ 1 (* 8 h)))) 4)))
    (isInteger solution)))

(defun HexagonalNumber (n)
  (* n (- (* 2 n) 1)))

(defun TriangleNumber (n)
  (* (/ n 2) (+ n 1)))

(defun problem45 (n)
  (let ((trinum (triangleNumber n)))
    (if (and (isPentagonalNumber2 trinum)
	     (isHexagonalNumber trinum))
	(list trinum n)
	(problem45 (1+ n)))))

(problem45 300)