freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/rosetta-code/lychrel-numbers.md

id, title, challengeType, forumTopicId, dashedName

id	title	challengeType	forumTopicId	dashedName
5ea2815a8640bcc6cb7dab3c	Lychrel numbers	5	385287	lychrel-numbers

--description--

1. Take an integer n₀, greater than zero.
2. Form the next number n of the series by reversing n₀ and adding it to n₀
3. Stop when n becomes palindromic - i.e. the digits of n in reverse order == n.

The above recurrence relation when applied to most starting numbers n = 1, 2, ... terminates in a palindrome quite quickly.

For example if n₀ = 12 we get:

12
12 + 21 = 33,  a palindrome!

And if n₀ = 55 we get:

55
55 + 55 = 110
110 + 011 = 121,  a palindrome!

Notice that the check for a palindrome happens after an addition.

Some starting numbers seem to go on forever; the recurrence relation for 196 has been calculated for millions of repetitions forming numbers with millions of digits, without forming a palindrome. These numbers that do not end in a palindrome are called Lychrel numbers.

For the purposes of this task a Lychrel number is any starting number that does not form a palindrome within 500 (or more) iterations.

Seed and related Lychrel numbers:

Any integer produced in the sequence of a Lychrel number is also a Lychrel number.

In general, any sequence from one Lychrel number might converge to join the sequence from a prior Lychrel number candidate; for example the sequences for the numbers 196 and then 689 begin:

    196
    196 + 691 = 887
    887 + 788 = 1675
    1675 + 5761 = 7436
    7436 + 6347 = 13783
    13783 + 38731 = 52514
    52514 + 41525 = 94039
    ...
    689
    689 + 986 = 1675
    1675 + 5761 = 7436
    ...

So we see that the sequence starting with 689 converges to, and continues with the same numbers as that for 196.

Because of this we can further split the Lychrel numbers into true Seed Lychrel number candidates, and Related numbers that produce no palindromes but have integers in their sequence seen as part of the sequence generated from a lower Lychrel number.

--instructions--

Write a function that takes a number as a parameter. Return true if the number is a Lynchrel number. Otherwise, return false. Remember that the iteration limit is 500.

--hints--

isLychrel should be a function.

assert(typeof isLychrel === 'function');

isLychrel(12) should return a boolean.

assert(typeof isLychrel(12) === 'boolean');

isLychrel(12) should return false.

assert.equal(isLychrel(12), false);

isLychrel(55) should return false.

assert.equal(isLychrel(55), false);

isLychrel(196) should return true.

assert.equal(isLychrel(196), true);

isLychrel(879) should return true.

assert.equal(isLychrel(879), true);

isLychrel(44987) should return false.

assert.equal(isLychrel(44987), false);

isLychrel(7059) should return true.

assert.equal(isLychrel(7059), true);

--seed--

--seed-contents--

function isLychrel(n) {

}

--solutions--

function isLychrel(n) {
  function reverse(num) {
    return parseInt(
      num
        .toString()
        .split('')
        .reverse()
        .join('')
    );
  }

  var i;
  for (i = 0; i < 500; i++) {
    n = n + reverse(n);
    if (n == reverse(n)) break;
  }

  return i == 500;
}