Honaker Prime Number is a prime number P such that the sum of digits of P and sum of digits of index of P is a Prime Number.
Few Honaker Prime Numbers are:
131, 263, 457, 1039, 1049, 1091, 1301, 1361, 1433, 1571, 1913, 1933, 2141, 2221,…
Check if N is a Honaker Prime Number
Given an integer N, the task is to check if N is a Honaker Prime Number or not. If N is an Honaker Prime Number then print “Yes” else print “No”.
Examples:
Input: N = 131
Output: Yes
Explanation:
Sum of digits of 131 = 1 + 3 + 1 = 5
Sum of digits of 32 = 3 + 2 = 5Input: N = 161
Output: No
Approach: The idea is to find the index of the given number and check if sum of digits of index and N is the same or not. If it is same then, N is an Honaker Prime Number and print “Yes” else print “No”.
C++
// C++ program for the above approach#include <bits/stdc++.h>#define limit 10000000using namespace std;int position[limit + 1];// Function to precompute the position// of every prime number using Sievevoid sieve(){ // 0 and 1 are not prime numbers position[0] = -1, position[1] = -1; // Variable to store the position int pos = 0; for (int i = 2; i <= limit; i++) { if (position[i] == 0) { // Incrementing the position for // every prime number position[i] = ++pos; for (int j = i * 2; j <= limit; j += i) position[j] = -1; } }}// Function to get sum of digitsint getSum(int n){ int sum = 0; while (n != 0) { sum = sum + n % 10; n = n / 10; } return sum;}// Function to check whether the given number// is Honaker Prime number or notbool isHonakerPrime(int n){ int pos = position[n]; if (pos == -1) return false; return getSum(n) == getSum(pos);}// Driver Codeint main(){ // Precompute the prime numbers till 10^6 sieve(); // Given Number int N = 121; // Function Call if (isHonakerPrime(N)) cout << "Yes"; else cout << "No";} |
Java
// Java program for above approach class GFG{ static final int limit = 10000000; static int []position = new int[limit + 1]; // Function to precompute the position // of every prime number using Sieve static void sieve() { // 0 and 1 are not prime numbers position[0] = -1; position[1] = -1; // Variable to store the position int pos = 0; for (int i = 2; i <= limit; i++) { if (position[i] == 0) { // Incrementing the position for // every prime number position[i] = ++pos; for (int j = i * 2; j <= limit; j += i) position[j] = -1; } } } // Function to get sum of digitsstatic int getSum(int n){ int sum = 0; while (n != 0) { sum = sum + n % 10; n = n / 10; } return sum;}// Function to check whether the given number// is Honaker Prime number or notstatic boolean isHonakerPrime(int n){ int pos = position[n]; if (pos == -1) return false; return getSum(n) == getSum(pos);}// Driver code public static void main(String[] args) { // Precompute the prime numbers till 10^6 sieve(); // Given Number int N = 121; // Function Call if (isHonakerPrime(N)) System.out.print("Yes\n"); else System.out.print("No\n"); } } // This code is contributed by shubham |
Python3
# Python3 program for the above approach limit = 10000000position = [0] * (limit + 1)# Function to precompute the position # of every prime number using Sieve def sieve(): # 0 and 1 are not prime numbers position[0] = -1 position[1] = -1 # Variable to store the position pos = 0 for i in range(2, limit + 1): if (position[i] == 0): # Incrementing the position for # every prime number pos += 1 position[i] = pos for j in range(i * 2, limit + 1, i): position[j] = -1# Function to get sum of digits def getSum(n): Sum = 0 while (n != 0): Sum = Sum + n % 10 n = n // 10 return Sum# Function to check whether the given# number is Honaker Prime number or not def isHonakerPrime(n): pos = position[n] if (pos == -1): return False return bool(getSum(n) == getSum(pos))# Driver code# Precompute the prime numbers till 10^6 sieve() # Given Number N = 121# Function Call if (isHonakerPrime(N)): print("Yes")else: print("No")# This code is contributed by divyeshrabadiya07 |
C#
// C# program for above approach using System;class GFG{ static readonly int limit = 10000000; static int []position = new int[limit + 1]; // Function to precompute the position // of every prime number using Sieve static void sieve() { // 0 and 1 are not prime numbers position[0] = -1; position[1] = -1; // Variable to store the position int pos = 0; for (int i = 2; i <= limit; i++) { if (position[i] == 0) { // Incrementing the position for // every prime number position[i] = ++pos; for (int j = i * 2; j <= limit; j += i) position[j] = -1; } } } // Function to get sum of digitsstatic int getSum(int n){ int sum = 0; while (n != 0) { sum = sum + n % 10; n = n / 10; } return sum;}// Function to check whether the given number// is Honaker Prime number or notstatic bool isHonakerPrime(int n){ int pos = position[n]; if (pos == -1) return false; return getSum(n) == getSum(pos);}// Driver code public static void Main(String[] args) { // Precompute the prime numbers till 10^6 sieve(); // Given Number int N = 121; // Function Call if (isHonakerPrime(N)) Console.Write("Yes\n"); else Console.Write("No\n"); } } // This code is contributed by 29AjayKumar |
Javascript
<script>// Javascript program for above approach const limit = 10000000; let position = Array(limit + 1).fill(0); // Function to precompute the position // of every prime number using Sieve function sieve() { // 0 and 1 are not prime numbers position[0] = -1; position[1] = -1; // Variable to store the position let pos = 0; for (let i = 2; i <= limit; i++) { if (position[i] == 0) { // Incrementing the position for // every prime number position[i] = ++pos; for (let j = i * 2; j <= limit; j += i) position[j] = -1; } } } // Function to get sum of digits function getSum( n) { let sum = 0; while (n != 0) { sum = sum + n % 10; n = parseInt(n / 10); } return sum; } // Function to check whether the given number // is Honaker Prime number or not function isHonakerPrime( n) { let pos = position[n]; if (pos == -1) return false; return getSum(n) == getSum(pos); } // Driver code // Precompute the prime numbers till 10^6 sieve(); // Given Number let N = 121; // Function Call if (isHonakerPrime(N)) document.write("Yes\n"); else document.write("No\n");// This code is contributed by aashish1995 </script> |
Output:
No
Reference: https://oeis.org/A033548
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