Generalized Algorithm on idiosyncrasy of Numbers

In this paper, using computer algebra system a new generalized algorithm is developed to study and generalize the Kaprekar’s operation which can be used for desired numbers of iterations and is also applicable to any n-digits number which is greater than or equal to two. Existing relevant results are verified with the available results in literature and further extended to examine the difference (kernel) of the obtained number during the process with the number obtained in preceding iteration after each step. Sum of the digits of an acquired number obtained after each step is also noticed and found that sum of its digits is divisible by 9. A detailed investigation is conducted for all two-digit number and the output acquired is exhibited in tabular form which has not been studied in earlier. An 8-digits number also considered and found that it does not converges to a unique kernel like 3-digits and 4-digits, but follows a regular pattern after initial iteration. Analytical illustrations are provided along with pictorial representations for 2-digits, 3-digits 4-digits and 8-digits number. This algorithm can further be employed for numbers having any number of digits.