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Pankaj Gupta Scholar

2 weeks ago

Program to Check for Keith Number

A Keith number is an n-digit number that appears as a term in a sequence, where the first n terms are its own digits, and each following term is the sum of the previous n terms. For example, 197 is a Keith number because starting with 1, 9, 7, and continually adding the last three terms together, 197 appears in the sequence: 1, 9, 7, 17, 33, 57, 107, 197

Program: 

import java.io.*;
class Keith {
public static void main(String args[]) throws IOException {
BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
System.out.print(“Enter the number : “); // inputting the number
int n = Integer.parseInt(br.readLine());
int c = n;
String s = Integer.toString(n);
int d = s.length(); // finding the number of digits (d) in the number
int arr[] = new int[d]; // array for storing the terms of the series

for(int i = d – 1; i >= 0; i–) {
arr[i] = c % 10; // storing the digits of the number in the array
c = c / 10;
}

int sum = 0;
while(sum < n) {
sum = 0;
for(int j = 0; j < d; j++) {
sum = sum + arr[j];
}
for(int j = 0; j < d – 1; j++) {
arr[j] = arr[j + 1];
}
arr[d – 1] = sum;
}

if(sum == n)
System.out.println(“The number is a Keith Number”);
else
System.out.println(“The number is not a Keith Number”);
}
}

How this program works

Program Breakdown

• The program imports necessary classes for input handling.

• It reads an integer n from the user.

• It determines the number of digits d in n (using string conversion and length).

• It creates an array arr to store the digits of the number in order.

• It fills this array with the individual digits of n.

Sequence Generation

• The heart of the logic is the while loop, which keeps generating new terms in the sequence by summing the elements of the array.

• Each time, after summing, the digits in the array are shifted left (removing the oldest digit), and the new sum is appended to the end.

• This loop continues until the sum reaches or exceeds n.

Final Check

• If the sequence hits exactly n, then it is a Keith number, so “The number is a Keith Number” is printed.

• If not, it’s not a Keith number.

Key Points in the Example Code

• Let’s say the input is 197: it will fill the array as , then produce 17, 33, 57, 107, and finally 197.​

• If the number appears in its sequence, it’s a Keith number.

Typical Output

• If the input is 197, output is: The number is a Keith Number.

• If the input is 12, output is: The number is not a Keith Number.​

This process helps determine if a number belongs to this interesting mathematical set.

Pankaj Gupta Scholar

1 year ago

Program to Check for A Disarium number

A Disarium number is a number where the sum of its digits powered with their respective positions is equal to the number itself. For example, 175 is a Disarium number because: $1^1+7^2+5^3=1+49+125=1751^1\; +\; 7^2\; +\; 5^3\; =\; 1\; +\; 49\; +\; 125\; =\; 175$. Here’s a simple Java program to check if a number is a Disarium number: 

import java.util.Scanner;
public class DisariumNumber
{ // Method to calculate the number of digits in a number
public static int countDigits(int number)
{ int count = 0;
while (number != 0)
{ count++;
number /= 10;
}
return count;
}

// Method to check if the number is Disarium

public static boolean isDisarium(int number)
{ int sum = 0, temp = number;
int digits = countDigits(number);
// Calculate sum of digits powered by their respective positions
while (temp != 0)
{ int digit = temp % 10;
sum += Math.pow(digit, digits--);
temp /= 10;
}
// Return true if sum equals the original number
return sum == number;
}
public static void main(String[] args)
{ Scanner scanner = new Scanner(System.in);
System.out.print("Enter a number: ");
int number = scanner.nextInt();
if (isDisarium(number))
{ System.out.println(number + " is a Disarium number."); }
else
{ System.out.println(number + " is not a Disarium number."); }
scanner.close();
}
}

How the program works

1. The countDigits method counts how many digits are in the number.
2. The isDisarium method calculates the sum of each digit raised to the power of its position (starting from 1).
3. The main method prompts the user for a number, checks if it’s a Disarium number, and outputs the result.