Euler Project 30

Surprisingly there are only three numbers that can be written as the sum of fourth powers of their digits:

1634 = 1⁴ + 6⁴ + 3⁴ + 4⁴
8208 = 8⁴ + 2⁴ + 0⁴ + 8⁴
9474 = 9⁴ + 4⁴ + 7⁴ + 4⁴

As 1 = 1⁴ is not a sum it is not included.

The sum of these numbers is 1634 + 8208 + 9474 = 19316.

Find the sum of all the numbers that can be written as the sum of fifth powers of their digits.

My Solution

(defun enumerate-interval (low high)

(loop for i from low to high

collect i))

(defun fifthpower(n)

(let ((numberstr (format nil "~a" n)))

(loop for i from 0 to (- (length numberstr) 1)

sum (expt (parse-integer numberstr :start i :end (+ i 1)) 5))))

(defun Euler30()

(remove-if-not #'(lambda(x) (= x (fifthpower x))) (enumerate-interval 1 9999999)))

(apply #'+ (Euler30))

Others' Solution

First Solution

(defun digits (num)
(map 'list
#'(lambda (char) (read-from-string (string char)))
(prin1-to-string num)))

(defun digit-power (num power)
(reduce #'+ (map 'list #'(lambda (n) (expt n power)) (digits num))))

(defun sum-of-digit-powers (power)
(let ((limit (loop for i from 1
for j = (* i (expt 9 power))
when (< j (expt 10 i))
return j)))
(loop for i from 2 to limit
when (= i (digit-power i power))
sum i)))

(defun euler30 ()
(sum-of-digit-powers 5))

Second Solution

(defun digit-sum (n fn)
(labels ((f-s (n res)
(if (zerop n)
res
(f-s (floor n 10) (+ res (funcall fn (mod n 10)))))))
(f-s n 0)))

(defun math-30 ()
"Find the sum of all numbers which are equal to the sum of 5th power of their digits"
(do ((i 2 (1+ i))
(result 0 (if (= i (digit-sum i #'(lambda (n) (expt n 5)))) (+ result i) result)))
((> i 360000) result)))