196-Algorithm: Palindromic Numbers

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This Demonstration is an exploration and display of the 196-algorithm, which consists of taking a number, reversing its digit order, and then adding the result to the original value. The result tends to get one closer to a palindromic number (a palindromic number reads the same from left to right as from right to left, e.g. 1122211). The number 196 does not generate a palindromic number for at least 2,400,000 iterations.

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The recording table keeps track of the last 10 entries. Click the "iterate" button to apply the algorithm once to the current number. The "jump" button lets you apply the algorithm up to 200 times with one click; it automatically stops once a palindromic number is reached. You can change the jump limit with the slider. If you change the initial number, both the iteration count and the table automatically reset. To reset manually, simply click the "reset" button.

Certain numbers (called Lychrel numbers) have not been found to generate a palindromic number as of yet; an example is 196, for which the algorithm is named.

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Contributed by: Vladimir Feinberg (February 2012)
Open content licensed under CC BY-NC-SA


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