Problem 055: Lychrel numbers
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
How many Lychrel numbers are there below ten-thousand?
NOTE: Wording was modified slightly on 24 April 2007 to emphasise the theoretical nature of Lychrel numbers.
0 v/+55\+g01\p01%+< $ v/+55\+g01\p01%+<
>"}P"*>::0\>:!#v_\55+*\:55 ^>:!#v_\::0\>:!#v_\55+*\:55 ^
>$ .@ >$+38* #v ^# < |-p02:$<
Not much to say about this one. I reuse the isPalindrome code from P-36 and bruteforce through all the numbers.
I think it would be really useful to cache the intermediate results - but our befunge space is too small for such data structures :/
|Interpreter steps:||10 470 329|
|Execution time (BefunExec):||2.22s (4.73 MHz)|
|Program size:||56 x 5 (fully conform befunge-93)|