Solutions for Project Euler problems

euler.lisp

;(compile-file "euler.lisp")

(defun fib (n)
  (if (or (= n 0)
	  (= n 1))
      1
      (+ (fib (- n 1))
	 (fib (- n 2)))))

(defun square (number)
  "square an integer"
  (* number number))

(defun p1 (number)
  "Add all natural numbers below 'number' that are multiples of 3 or 5"
  (loop for i from 0 to (- number 1)
       when (or (= (mod i 3) 0)
		(= (mod i 5) 0))
       sum i))

(defun p2 (number)
  "find the sum of all even terms of the fibonnaci sequence less than number"
  (loop for i from 2
       while (<= (fib i) number)
       when (evenp (fib i)) sum (fib i)))

(defun p3 (number)
  "Find largest prime factor of number"
  (loop for i from 2 to (ceiling (sqrt number))
       when (= (mod number i) 0)
       collect i))

(defun p4 ()
  "Find the largest palindrome that is a product of two 3-digit numbers"
  (loop for i from 100 to 999
     maximize (loop for j from 100 to 999
		 when (equalp (write-to-string (* i j))
			      (reverse (write-to-string (* i j))))
		 maximize (* i j))))

(defun p6 (n)
  "difference between sum of squares and square of sums from 1 to n"
  (- (square (loop for i from 1 to n
		  sum i))
     (reduce #'+
	     (mapcar #'square
		     (loop for i from 1 to n
			  collect i)))))

(defun divisible-by (number list)
  "return true if divisible by an element in the list"
  (loop for i in list
       thereis (= (mod number i) 0)))

(defun prime-list-generator (current max-value prime-list)
  "business end of p10"
  (if (= current max-value)
      prime-list
      (if (divisible-by current prime-list)
	  (prime-list-generator (+ current 1) max-value prime-list)
	  (prime-list-generator (+ current 1) max-value (nconc prime-list (list current))))))

(defun p10 (n)
  "Find the sum of all the primes below n"
  (reduce #'+ (prime-list-generator 2 n '())))

(defun p48 ()
  "Find the last 10 digits of 1^1 + 2^2 + 3^3 + ... + n^n"
  (mod (loop for x from 1 to 1000 sum (expt x x)) (expt 10 10)))