Given an integer N, the task is to count the number of ways so that N can be written as the sum of a prime number and twice of a square, i.e. , where P can be any prime number and A is any positive integer.
Input: N = 9
9 can be represented as sum of prime number and twice a square in only one way –
Input: N = 15
15 can be represented as sum of prime number and twice a square in two ways –
Approach: The idea is to use Seive of Eratosthenes to find all the primes and then for each prime number check for every possible number starting from 1. If any prime number and twice a square is equal to the given number then increment the count of the number of ways by 1.
Below is the implementation of the above approach:
- Count of ways to split a given number into prime segments
- Number of distinct ways to represent a number as sum of K unique primes
- Represent a number as a sum of maximum possible number of Prime Numbers
- Count of integers up to N which represent a Binary number
- Count of matchsticks required to represent the given number
- Count occurrences of a prime number in the prime factorization of every element from the given range
- Different ways to represent N as sum of K non-zero integers
- Quick ways to check for Prime and find next Prime in Java
- Count number of ways to get Odd Sum
- Count number of ways to divide a number in 4 parts
- Count ways to express even number ‘n’ as sum of even integers
- Count number of ways to arrange first N numbers
- Count number of ways to cover a distance | Set 2
- Count ways to express a number as sum of exactly two numbers
- Count of prime digits of a Number which divides the number
- Count ways to express a number as sum of consecutive numbers
- Count number of ways to reach a given score in a Matrix
- Count the number of ways to construct the target string
- Count ways to spell a number with repeated digits
- Count the number of ways to divide N in k groups incrementally
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