
# -*- coding: utf-8 -*-
'''
    File name: code\primesum_numbers\sol_543.py
    Author: <NAME>
    Date created: Oct 20, 2018
    Python Version: 3.x
'''

# Solution to Project Euler Problem #543 :: Prime-Sum Numbers
# 
# For more information see:
# https://projecteuler.net/problem=543

# Problem Statement 
'''
Define function P(n,k) = 1 if n can be written as the sum of k prime numbers (with repetitions allowed), and P(n,k) = 0 otherwise.

For example, P(10,2) = 1 because 10 can be written as either 3 + 7 or 5 + 5, but P(11,2) = 0 because no two primes can sum to 11.

Let S(n) be the sum of all P(i,k) over 1 ≤ i,k ≤ n.

For example, S(10) = 20, S(100) = 2402, and S(1000) = 248838.

Let F(k) be the kth Fibonacci number (with F(0) = 0 and F(1) = 1).

Find the sum of all S(F(k)) over 3 ≤ k ≤ 44
'''

# Solution 

# Solution Approach 
'''
'''


# -*- coding: utf-8 -*-
'''
    File name: code\primesum_numbers\sol_543.py
    Author: <NAME>
    Date created: Oct 20, 2018
    Python Version: 3.x
'''

# Solution to Project Euler Problem #543 :: Prime-Sum Numbers
# 
# For more information see:
# https://projecteuler.net/problem=543

# Problem Statement 
'''
Define function P(n,k) = 1 if n can be written as the sum of k prime numbers (with repetitions allowed), and P(n,k) = 0 otherwise.

For example, P(10,2) = 1 because 10 can be written as either 3 + 7 or 5 + 5, but P(11,2) = 0 because no two primes can sum to 11.

Let S(n) be the sum of all P(i,k) over 1 ≤ i,k ≤ n.

For example, S(10) = 20, S(100) = 2402, and S(1000) = 248838.

Let F(k) be the kth Fibonacci number (with F(0) = 0 and F(1) = 1).

Find the sum of all S(F(k)) over 3 ≤ k ≤ 44
'''

# Solution 

# Solution Approach 
'''
'''

# -*- coding: utf-8 -*- File name: code\primesum_numbers\sol_543.py     Author: <NAME>     Date created: Oct 20, 2018     Python Version: 3.x # Solution to Project Euler Problem #543 :: Prime-Sum Numbers # # For more information see: # https://projecteuler.net/problem=543 # Problem Statement Define function P(n,k) = 1 if n can be written as the sum of k prime numbers (with repetitions allowed), and P(n,k) = 0 otherwise.  For example, P(10,2) = 1 because 10 can be written as either 3 + 7 or 5 + 5, but P(11,2) = 0 because no two primes can sum to 11.  Let S(n) be the sum of all P(i,k) over 1 ≤ i,k ≤ n.  For example, S(10) = 20, S(100) = 2402, and S(1000) = 248838.  Let F(k) be the kth Fibonacci number (with F(0) = 0 and F(1) = 1).  Find the sum of all S(F(k)) over 3 ≤ k ≤ 44 # Solution # Solution Approach