• KAPREKAR CONSTANT REVISITED
Abstract
Given a n digits number where not all the digits are same, we arrange the digits in increasing order and let us denote this number by i(n). Similarly arrange the given n digits in decreasing order and let us denote this number by d(n). Define the Kaprekar function, k(n) by k(n)=d(n)−i(n). If this new number has less than n digits, we add necessary 0’s on the left of k(n) to make it a n digits number. Then we keep repeat this process, that is we consider the sequence
D.R Kaprekar considered the case for n=4 and showed that the above sequence eventually becomes a constant and that magical constant is 6174 no matter what the four digits number you have started with. In this paper we will investigate this sequence for n=3 and n=4. We will also summarize some known results for some other values of “n”.
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