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.
Here is the program to print first 25 pernicious number.
Below is the implementation of the above approach.
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
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Improved By : Mithun Kumar