Pernicious number

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 .

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 using namespace std;    // function to check prime number 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 void printPernicious(int n) {     for (int i=1,count=0; count

Java

 // Java program to print first // n pernicious numbers import 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

Python3

 # Python program to print # first n pernicious numbers    # function to check  # prime number def 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 # numbers def 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 Code n = 25 printPernicious(n)    # This code is contributed by Ansu Kumari

C#

 // C#program to print first // n pernicious numbers using 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

PHP

 > 1;     }        return \$count; }    // Prints first n Pernicious numbers function 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  ?>

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

References :
Wiki

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