A pernicious number is a positive integer which has prime number of ones in its binary representation. The first pernicious number is 3 since 3 = (11)(in binary representation) and 1 + 1 = 2, which is a prime.
Properties of Pernicious Numbers :
1. There isn’t any pernicious number which is also power of 2 because powers of two in binary form are represented as a one followed by zeros. So, 1 is not considered as a prime number.
2. Every number of the form 
+ 1 with n > 0 is a pernicious number as the number of ones in binary form is 2 which is prime.
3. A number of the form – 1 with prime p is a pernicious number known as a Mersenne number .
The idea to print first n Pernicious numbers is simple.
Do following for every number from 1 to n.
1) Count set bits in current number
2) Print current number if count of set bits is prime. We use simple primality check for this purpose.
Here is the program to print first 25 pernicious number.
Below is the implementation of the above approach.
C++
// CPP program to print first n pernicious numbers#include <bits/stdc++.h>using namespace std;// function to check prime numberbool isPrime(int x){ if (x < 2) return false; for (int i = 2; i < x; i++) { if (x % i == 0) return false; } return true;}// Prints first n Pernicious numbersvoid printPernicious(int n){ for (int i=1,count=0; count<n; i++) { // "__builtin_popcount(i)" count no // of ones in binary representation if (isPrime(__builtin_popcount(i))) { cout << i << " "; count++; } }}int main(){ int n = 25; printPernicious(n); return 0;} |
Java
// Java program to print first// n pernicious numbersimport java.util.*;class GFG { // function to count no of // ones in binary representation static int countSetBits(int n) { int count = 0; while (n > 0) { n &= (n - 1) ; count++; } return count; } // function to check prime number static boolean isPrime(int x) { if (x < 2) return false; for (int i = 2; i < x; i++) { if (x % i == 0) return false; } return true; } // Prints first n Pernicious numbers static void printPernicious(int n) { for (int i=1,count=0; count<n; i++) { if (isPrime(countSetBits(i))) { System.out.print( i + " "); count++; } } } // Driver Code public static void main (String[] args) { int n = 25; printPernicious(n); }}// This code is contributed by Ansu Kumari |
Python3
# Python program to print# first n pernicious numbers# function to check # prime numberdef isPrime(x): if x < 2: return False for i in range(2, x): if not x % i: return False return True# Prints first n Pernicious# numbersdef printPernicious(n): i, count = 1, 0 while count < n: # "bin(i).count('1')" count # no of ones in binary # representation if (isPrime(bin(i).count('1'))): print(i, end=' ') count += 1 i += 1# Driver Coden = 25printPernicious(n)# This code is contributed by Ansu Kumari |
C#
// C#program to print first// n pernicious numbersusing System;class GFG { // function to count no of // ones in binary representation static int countSetBits(int n) { int count = 0; while (n > 0) { n &= (n - 1) ; count++; } return count; } // function to check prime number static bool isPrime(int x) { if (x < 2) return false; for (int i = 2; i < x; i++) { if (x % i == 0) return false; } return true; } // Prints first n Pernicious numbers static void printPernicious(int n) { for (int i=1,count=0; count<n; i++) { if (isPrime(countSetBits(i))) { Console.Write( i + " "); count++; } } } // Driver Code public static void Main () { int n = 25; printPernicious(n); }}// This code is contributed by vt_m |
PHP
<?php// PHP program to print first// n pernicious numbers// function to check prime numberfunction isPrime($x){ if ($x < 2) return false; for ($i = 2; $i < $x; $i++) { if ($x % $i == 0) return false; } return true;}//this function count no of // ones in binary representationfunction getBitCount($value){ $count = 0; while($value) { $count += ($value & 1); $value = $value >> 1; } return $count;}// Prints first n Pernicious numbersfunction printPernicious($n){ for ($i = 1, $count = 0; $count < $n; $i++) { //count no of ones in // binary representation if (isPrime(getBitCount($i))) { echo $i." "; $count++; } }}// Driver code$n = 25;printPernicious($n);// This code is contributed by mits ?> |
Javascript
<script>// JavaScript program to print first// n pernicious numbers // function to count no of // ones in binary representation function countSetBits(n) { let count = 0; while (n > 0) { n &= (n - 1) ; count++; } return count; } // function to check prime number function isPrime(x) { if (x < 2) return false; for (let i = 2; i < x; i++) { if (x % i == 0) return false; } return true; } // Prints first n Pernicious numbers function printPernicious(n) { for (let i=1,count=0; count<n; i++) { if (isPrime(countSetBits(i))) { document.write( i + " "); count++; } } }// Driver code let n = 25; printPernicious(n);</script> |
Output :
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36
Time Complexity: O(nlogn)
Space Complexity: O(1)
References :
Wiki
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