# 196-Algorithm (palindromic numbers)

• Curvation
In summary, the 196-Algorithm is a mathematical procedure where any positive integer is reversed and added to the original number, repeating the process until a palindromic number is produced. There are computer programs available to automate this process, and there are also websites dedicated to exploring this problem. While it may not have practical application, it is a fascinating concept to study.
Curvation
I recently read about the 196-Algorithm problem and i found it extremely interesting.
Do you know if there is a computer programme which automatically does the operation of the reverse-then-add sequence and then repeat the procedure with the sum so obtained, checking of course if the number that has being produced is a palindromic number?

P.S. Sorry in advance for my English.

The 196 Algorithm is:
Take any positive integer of two digits or more, reverse the digits, and add to the original number. This is the operation of the reverse-then-add sequence. Now repeat the procedure with the sum so obtained. This procedure quickly produces palindromic numbers for most integers.
For example, starting with the number 5280 produces the sequence 5280, 6105, 11121, 23232. The end results of applying the algorithm to 1, 2, 3, ... are 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 11, 33, 44, 55, 66, 77, 88, 99, 121, ... The value for 89 is especially large, being 8813200023188.

Curvation said:
I recently read about the 196-Algorithm problem and i found it extremely interesting.
Do you know if there is a computer programme which automatically does the operation of the reverse-then-add sequence and then repeat the procedure with the sum so obtained, checking of course if the number that has being produced is a palindromic number?

P.S. Sorry in advance for my English.
Since the 196=Algorithm uses basic math operations it would be a fairly simple algorithm to program. I did a web search using "196 algorithm C++" and discovered http://users.tmok.com/~pla/lychrel/lychrel.shtml which is a nice discussion of the algorithm. 196 is the first of many, the so call "Lychrel numbers" that don't seem to become palindromic using the algorithm. There also are links for downloading the better known (speedier) 196-algorithm computer programs.

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Also after searching the term Lychrel, I guess that I should mention http://www.p196.org which site acts as a home page for those interested in this problem. It also has a page which rates the computer programs submitted for investigating this problem and many other useful links.
Although I think that the search for Lychel numbers is about as interesting as the search for primes, there is no known usefulness in it.

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Thanks ramsay.
Very interesting sites.
This is my first approach to study number theory and programming.
Yes of course search for primes is very useful but one step at a time...
Thanks a lot.

## 1. What is the 196-Algorithm?

The 196-Algorithm is a mathematical process used to determine whether a number is a palindromic number or not. A palindromic number is a number that reads the same backward as forward, such as 121 or 1331.

## 2. How does the 196-Algorithm work?

The 196-Algorithm works by reversing the digits of a number and then adding it to the original number. This process is repeated until a palindromic number is obtained or the number reaches 196. If the number reaches 196 and is still not a palindromic number, it is considered a non-Lychrel number.

## 3. What are Lychrel numbers?

Lychrel numbers are numbers that never form a palindromic number when the 196-Algorithm is applied. These numbers are considered to be very rare, and their existence is still a topic of research and debate among mathematicians.

## 4. Can the 196-Algorithm be applied to any number?

Yes, the 196-Algorithm can be applied to any positive integer. However, larger numbers may require a significant amount of computation time to determine whether they are palindromic or not.

## 5. How is the 196-Algorithm useful in real-life applications?

The 196-Algorithm has various applications in different fields, such as cryptography, data compression, and error-correcting codes. It is also used in programming and software development to check for palindromic numbers or to generate them for specific purposes.

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