Step by Step solution about How to resolve the algorithm Kaprekar numbers step by step in the Mathematica/Wolfram Language programming language

This Wolfram code defines a function, KaprekaQ, to check if a positive integer n is a Kaprekar number, and uses it to find and count Kaprekar numbers within a given range.

Kaprekar Number: A Kaprekar number is one whose square, when written as a string, can be split into two parts that add up to the original number. For example, 9 is a Kaprekar number because 9^2 = 81, and 8 + 1 = 9.

Code Explanation:

1. KaprekaQ[n_Integer] Function:

   • This function takes an integer n as input and returns True if n is a Kaprekar number, and False otherwise.
   • It calculates n^2 and converts it to a list of digits data.
   • It iterates through data from the second digit onwards, checking if the digits from the current position to the end are not all zeros.
   • If they are not zeros, the function adds the digits before and after the current position and checks if their sum equals n.
   • If the sum equals n, the function sets last to True to indicate that n is a Kaprekar number.

2. Kaprekar Number Selection:

   • The code calls Select[Range[10000], KaprekaQ] to select Kaprekar numbers from the range 1 to 10000. This returns a list of Kaprekar numbers in that range.
   • Then, it counts the number of Kaprekar numbers in the range 1 to 1000000 by using Length[Select[Range[1000000], KaprekaQ]].

KaprekaQ[1] = True;
KaprekaQ[n_Integer] :=  Block[{data = IntegerDigits[n^2], last = False, i = 1},
  While[i < Length[data] && FromDigits[data[[i + 1 ;;]]] =!= 0 &&  Not[last],
   last = FromDigits[data[[;; i]]] + FromDigits[data[[i + 1 ;;]]] == n;
   i++]; last];
Select[Range[10000], KaprekaQ]
Length[Select[Range[1000000], KaprekaQ]]