## Palindromic Repetitions

Arithmetic, algebra, number theory, sequence and series, analysis, ...
jnmcd
Posts: 2
Joined: Wed Jan 07, 2015 2:45 am

### Palindromic Repetitions

A palindrome is a number that is the same way forward as it is backwards.
For example, 22 is a palindrome.
Clearly, however, 23 is not.
But by adding 23 reversed on to itself (32), you get 55, which is a palindrome.
That took 1 repetition.
With 64, 1 repetition gives you 110, and since that isn't a palindrome, you must do another repetition. You'll end up with 121, which is a palindrome.
That took 2 repetitions.
So my question is this:
What is the lowest number to require more than 25 repetitions to become a palindrome? (Yes, brute force will work)
pj6444
Posts: 9
Joined: Fri Jan 02, 2015 2:30 am

### Re: Palindromic Repetitions

Should we assume that all numbers will create a palindrome eventually? What if the number is already a palindrome to begin with?
NChaloult
Posts: 1
Joined: Tue Jan 05, 2016 1:29 am

### Re: Palindromic Repetitions

In the case of this problem, it would not matter if the theory that all numbers eventually arrive at a palindrome is later proven to be false, for we are only looking for the first one that takes more than 25 repetitions. Also, if a number already is a palindrome, then did it not take 0 repetitions to arrive at a palindrome? This is simply my thought process, at least...
jaap
Posts: 559
Joined: Tue Mar 25, 2008 3:57 pm
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