Alternative ways of finding palindromic numbers

[JT73]

^As the title says, I was curious if there are any alternative ways of finding palindromic numbers instead of using the reversal/add method?

Thanks

 

[Jamma]

Huh, do you mean "how can they crop up in maths"? Obviously it's easy to "find" any palindromic number- they will correspond to some number x where you stick x next to its reversed self or where you sit x next to its reversed self without the first digit.

e.g. 1524 --> 15244251
or 1524 -->1524251

Any palindromic number will be of this form.

 

[JT73]

I've seen the process for finding a palindromic number which is the reversal/add way. For example, 186 + 681 = 867+768= 1635. + 5361 = 6996 So 186 gets palindromic at 6996 after 3 steps.

People have created programs that do these reversal/add techniques to numbers and then show how many steps it took to get palindromic. http://mathforum.org/library/drmath/view/51508.html


However, a few numbers such at 196 even after 2 million steps has still not become palindromic. Is there any alternative ways of finding palindromic numbers by usuing a different process instead of the reversal/add?

 

[JT73]

...bueller?...bueller?

 

[CellCoree]

for your question! There are indeed alternative ways of finding palindromic numbers. One method is to use a digital root approach, where you repeatedly sum the digits of a number until you are left with a single digit. If the resulting digit is the same as the original number, then it is a palindromic number. Another method is to use a binary search approach, where you start with a large number and continually divide it in half until you find a palindromic number. Additionally, there are various mathematical formulas and algorithms that can be used to generate palindromic numbers. Ultimately, the most efficient method will depend on the specific requirements and constraints of the problem at hand.