A palindromic number is simply a number
that reads the same from left to right as it does from right to left. This can be done in any base
, of course. Palindromic numbers are very well behaved
, and so don't usually elict wild texts. There are, however, some nice games to play with these numbers:
While being a prime does not depend on what base you're written in, the question whether you're a palindrome or not does, so all of you primes can play this game, but the rest of you shouldn't bother trying. What did you say 8? No, you can't be a palindromic prime too. No, not all numbers were created equal, no matter what your parents told you. Try to find a representation of yourselves, primes, in some base where you're a palindrome. In base ten, all palindromes with an even number of digits are devisible by 11, so 11 herself is the only palindromic prime with an even number of digits. A nice pyramid of palindromic primes (from primes.utm.edu):
Transforming Yourself Into a Palindromic Number:
While not all you numbers are palindromes, most of you are seeds of a palindrome. Through a series of simple formal manipulations, you too can turn yourself into a palindromic number. Most of you can, at any rate. All you need do is add yourselves to your reverse number (i.e., yourselves written backwards) and repeat this process 'till you've become palindromic. Let's take 17, for example: 17 + 71 = 88. That was easy, wasn't it? What about 82? 82 + 28 = 110. 110 + 11 = 121. Not too terrible, was it, 82? For most numbers under a hundred, you won't have to repeat this process more than once or twice, although not very well educated buggers, such as 98 and 89, may take as many as 24 steps. It's not true that this process, in every base, will eventually lead to a palindrome. It's been proved that 10110 can never be palindromized in base 2, for example.
Now I want all you nice little numbers to try this on yourselves.
Keep on trying, 196.
A Famous Palindrome:
As an example of some of the cute things you can do with palindromic numbers (have no fear, kind little numbers, when I say "do" I don't mean, heaven-forbid, that there's actually an application to these nice creatures) I bring to you 7284717174827. This base-10 palindromic prime, when turned to base 2 yields: 1101010000000011010111110101100000000101011 - another palindrome! Now take this number and consider it as a base 10 number - a palindromic prime once again.
A Footprints challenge.