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196-Algorithm (palindromic numbers)

  1. Jan 31, 2008 #1
    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.
  2. jcsd
  3. Feb 1, 2008 #2
    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.
  4. Feb 1, 2008 #3
    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 [Broken] 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.
    Last edited by a moderator: May 3, 2017
  5. Feb 1, 2008 #4
    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: Feb 1, 2008
  6. Feb 1, 2008 #5
    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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