; If we take 47, reverse and add, 47 + 74 = 121, which is palindromic.
;
; Not all numbers produce palindromes so quickly. For example,
;
; 349 + 943 = 1292,
; 1292 + 2921 = 4213
; 4213 + 3124 = 7337
;
; That is, 349 took three iterations to arrive at a palindrome.
;
; Although no one has proved it yet, it is thought that some numbers, like 196,
; never produce a palindrome. A number that never forms a palindrome through
; the reverse and add process is called a Lychrel number. Due to the
; theoretical nature of these numbers, and for the purpose of this problem, we
; shall assume that a number is Lychrel until proven otherwise. In addition you
; are given that for every number below ten-thousand, it will either (i) become
; a palindrome in less than fifty iterations, or, (ii) no one, with all the
; computing power that exists, has managed so far to map it to a palindrome. In
; fact, 10677 is the first number to be shown to require over fifty iterations
; before producing a palindrome: 4668731596684224866951378664 (53 iterations,
; 28-digits).
;
; Surprisingly, there are palindromic numbers that are themselves Lychrel
; numbers; the first example is 4994.
;
; How many Lychrel numbers are there below ten-thousand?
;
; Answer: 249
(defn palindrom? [s]
(let [size (count s)
middle (int (/ size 2))
pre (.substring s 0 middle)
i (if (even? size) middle (inc middle))]
(= (list* pre) (reverse (.substring s i size)))))
(defn strrev [s]
(apply str (reverse s)))
(defn step [s]
(str (+ (bigint s) (bigint (strrev s)))))
(defn lychrel? [n]
(let [n (step (str n)) ; Don't count the number itself
lseq (take-while #(not (palindrom? %)) (iterate step n))]
(> (count (take 51 lseq)) 50)))
(prn (count (filter lychrel? (range 1 10000))))