A palindrome is a number that is the same when reversed, 2770772 for example. A palindrome can often be formed by adding a number to it's reverse: 641 + 146 = 787 (a palindrome). Using 78 as the seed, it takes 4 steps to produce a palindrome:
78 + 87 = 165
165 + 561 = 726
726 + 627 = 1353
1353 + 3531 = 4884 (a palindrome)
About 97% of integers less than 10,000 produce palindromes in less than 25 steps. A few, like 196 and 879, may never form palindromes.
Make a function that takes a palindrome as it's an argument and returns the smallest seed integer that will produce that palindrome, along with the number of steps required:
palSeq(palindrome) = [seed, steps]
palSeq(4884) ➞ [69, 4]
palSeq(1) ➞ [1, 0]
palSeq(11) ➞ [10, 1]
// 10 + 01 = 11
palSeq(3113) ➞ [199, 3]
palSeq(8836886388) ➞ [177, 15]
The sequence always terminates when the first palindrome is produced. If the seed is a palindrome, the sequence has 0 steps.