Keith Number in Java

In this java programming tutorial, you will learn about Keith Number and its implementation in java. It is frequently asked in Java coding.

What is Keith Number?

A positive n digit number x is called a Keith number or repfigit number (repetitive Fibonacci-like digit) if it is arranged in a special number sequence generated using its digits. This sequence has n terms as digit of x and the next term is determined by the sum of previous n terms and so on. And if the number x falls under this sequence then x is a Keith Number. Example: 19, 742, etc

Explanation: Consider the number 742. Go through the following steps:

First separate the digit, 7, 4, 2.

To find the next term, add the digits, 7+4+2 = 13
New Series: 7, 4, 2, 13.

To find the next term, add the last three digits of the above sequence, 13+2+4=19
New Series: 7, 4, 2, 13, 19.

To find the next term, add the last three digits of the above sequence, 19+13+2=34
New Series: 7, 4, 2, 13, 19, 34.

To find the next term, add the last three digits of the above sequence, 34+19+13=66
New Series: 7, 4, 2, 13, 19, 34, 66.

To find the next term, add the last three digits of the above sequence, 66+34+19=119
New Series: 7, 4, 2, 13, 19, 34, 66, 119.

To find the next term, add the last three digits of the above sequence, 119+66+34=219
New Series: 7, 4, 2, 13, 19, 34, 66, 119, 219.

To find the next term, add the last three digits of the above sequence, 219+119+66=404
New Series: 7, 4, 2, 13, 19, 34, 66, 119, 219, 404.

To find the next term, add the last three digits of the above sequence, 404+219+119=742
New Series: 7, 4, 2, 13, 19, 34, 66, 119, 219, 404, 742.

Now we will stop as we got the number 742 as the term of the series. Hence 742 is a Keith Number.

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What are the Steps to Find Keith Number with programming

1. Read a number (x).
2. Separate each digit from the number (x).
3. Add all the separated n-digits and that will give the next term of the series.
4. Again, add the last n-terms of the series to find the next term.
5. Repeat step 4 until the term which the same as the number(x).

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Java Program to check whether the Number is Keith Number or not

import java.util.Scanner;

public class KeithNumber
{
  public static void main(String[] args)
  {
    int i, sum = 0, n, num;
    Scanner sc = new Scanner(System.in);

    System.out.print("Enter a number: ");
    num = sc.nextInt();

    n = num;

    //string to get the length
    String s = Integer.toString(num);
    int d = s.length();
    int arr[] = new int[num];

    //separating the digit and storing it in array
    for (i = d - 1; i >= 0; i--)
    {
      arr[i] = n % 10;
      n = n / 10;

    }

    i = d;

    /*once the sum value becomes equal or greater than
    that of the entered number, it stops */
    while (sum < num)
    {
      sum = 0;
      for (int j = 1; j <= d; j++)
      {
        sum = sum + arr[i - j];
      }

      arr[i] = sum;
      i++;
    }

    //compares the sum with the entered number 
    if (sum == num)
      System.out.println(num + " is a Keith Number.");
    else
      System.out.println(num + " is not a Keith Number.");
  }
}

Output:

Enter a number: 742
742 is a Keith Number.

//Another output
Enter a number: 456
456 is not a Keith Number.

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Another way to do it, by creating a function that will pass Boolean value to the main function.

import java.util.*;

public class KeithNumber
{
  //function that checks if the given number is Keith or not  
  static boolean isKeithNum(int num)
  {
    //array list to store the separated digit 
    ArrayList<Integer> terms = new ArrayList<Integer> ();

    int temp = num, n = 0;	//n = no. of digits  

    //condition to separate the digit 
    while (temp > 0)
    {
      terms.add(temp % 10);
      temp = temp / 10;

      n++;
    }

    //reverse the List  
    Collections.reverse(terms);
    int next = 0, i = n;

    //calculation of next terms
    while (next < num)
    {
      next = 0;

      //condition for adding the terms to get new term
      for (int j = 1; j <= n; j++)
        next = next + terms.get(i - j);

      terms.add(next);
      i++;
    }

    /*now the next is either equal or greater than entered number
    if equal then it is true else false*/
    return (next == num);
  }

  //main 
  public static void main(String[] args)
  {
    int number;
    Scanner sc = new Scanner(System.in);

    System.out.print("Enter a number: ");
    number = sc.nextInt();

    //passing the number as an argument to the function  
    if (isKeithNum(number))
      System.out.println(number + " is a Keith number.");
    else
      System.out.println(number + " is not a Keith number.");

  }
}

Output:

Enter a number: 19
19 is a Keith number.

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