196-Algorithm (palindromic numbers)

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Discussion Overview

The discussion revolves around the 196-Algorithm, which involves a sequence of operations on numbers to determine if they can produce palindromic numbers. Participants explore the algorithm's mechanics, its implications regarding Lychrel numbers, and the availability of computer programs that can automate the process.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant inquires about existing computer programs that can perform the reverse-then-add sequence and check for palindromic results.
  • Another participant describes the 196-Algorithm and provides an example of its application, noting that it typically produces palindromic numbers for most integers.
  • A participant mentions that the 196-Algorithm is related to Lychrel numbers, which are numbers that do not seem to become palindromic through the algorithm.
  • Links to resources and discussions about the 196-Algorithm and Lychrel numbers are shared, highlighting the community interest in these topics.
  • There is a mention of the perceived lack of practical usefulness in the search for Lychrel numbers compared to prime number searches.

Areas of Agreement / Disagreement

Participants express interest in the 196-Algorithm and Lychrel numbers, but there is no consensus on the usefulness of studying Lychrel numbers compared to other mathematical pursuits. The discussion remains open regarding the effectiveness of the algorithm for all integers.

Contextual Notes

Some assumptions about the algorithm's behavior and the nature of Lychrel numbers remain unresolved. The discussion does not clarify the mathematical limits or conditions under which the algorithm operates effectively.

Who May Find This Useful

Individuals interested in number theory, programming, and mathematical curiosities may find this discussion relevant.

Curvation
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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.
 
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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.
 
Last edited:
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.
 

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