From 995bdf13b77f9c35f5ef8bcf3e764d2f5bfd35ca Mon Sep 17 00:00:00 2001
From: Julien Lengrand-Lambert <julien@lengrand.fr>
Date: Sun, 21 Oct 2012 19:55:59 +0200
Subject: [PATCH] Solves problem 44. a bit long but first guess was the right
 one

---
 README.markdown |  3 ++-
 e_44.py         | 64 +++++++++++++++++++++++++++++++++++++++++++++++++
 e_47.py         |  8 +++----
 3 files changed, 70 insertions(+), 5 deletions(-)
 create mode 100644 e_44.py

diff --git a/README.markdown b/README.markdown
index 64d3c44..b3d0b4a 100644
--- a/README.markdown
+++ b/README.markdown
@@ -60,6 +60,7 @@ So you may find some of the code here quite ugly. And this is the case :). Why o
 41 - What is the largest n-digit pandigital prime that exists? < 5 min <br />
 42 - Using words.txt, a 16K text file containing nearly two-thousand common English words, how many are triangle words? - < 1 sec <br />
 43 - Find the sum of all pandigital numbers with an unusual sub-string +divisibility property. - 28sec <br />
+44 - Find the smallest pair of pentagonal numbers whose sum and difference is pentagonal. **~= 19 min** <br />
 45 - Find the next triangle number that is also pentagonal and hexagonal. - < 1 sec <br />
 46 - What is the smallest odd composite that cannot be written as the sum of a prime and twice a square? - < 6 sec <br />
 48 - Find the last ten digits of 1^1 + 2^2 + ... + 1000^1000. - 0.053 <br />
@@ -82,4 +83,4 @@ Feel free to mail me for any comment or request.
 
 You can contact me at julien at lengrand dot fr, or on my [current website](http://www.lengrand.fr)
 
-Last update : 16/10/2012
+Last update : 21/10/2012
diff --git a/e_44.py b/e_44.py
new file mode 100644
index 0000000..61ae0f7
--- /dev/null
+++ b/e_44.py
@@ -0,0 +1,64 @@
+#!/usr/bin/env python
+'''
+Created on 21 oct. 2012
+
+@author: Julien Lengrand-Lambert
+
+DESCRIPTION: Solves problem 44 of Project Euler
+Pentagonal numbers are generated by the formula, Pn=n(3n1)/2.
+The first ten pentagonal numbers are:
+1, 5, 12, 22, 35, 51, 70, 92, 117, 145, ...
+
+It can be seen that P4 + P7 = 22 + 70 = 92 = P8.
+However, their difference, 70  22 = 48, is not pentagonal.
+
+Find the pair of pentagonal numbers, Pj and Pk,
+for which their sum and difference is pentagonal
+and D = |Pk - Pj| is minimised; what is the value of D?
+'''
+penta_vals = []
+
+
+def is_pentagonal(val):
+    """
+    Returns True if val is a pentagonal number
+    """
+    global penta_vals
+    return (val in penta_vals)
+
+
+def pent(val):
+    """
+    Returns the pentagonal number created using val
+    Pentagonal numbers are defined by Pn=n(3n-1)/2
+    """
+    return (val * (3 * val - 1) / 2)
+
+
+def create_pentagonal(ite=1000):
+    """
+    Returns a list of ite pentagonal numbers
+    default is 1000
+
+    Pentagonal numbers are defined by Pn=n(3n1)/2
+    """
+    temp = range(1, ite + 1)
+    return [pent(val) for val in temp]
+
+
+def find_pair(ite=1000):
+    """
+    Finds the pair of pentagonal numbers such as
+    Pj + Pk and Pj - Pk are also pentagonal
+    Returns minimised |Pk - Pj|
+    """
+    global penta_vals
+
+    penta_vals = create_pentagonal(ite)
+    for val_j in penta_vals:
+        for val_k in penta_vals:
+            if is_pentagonal(val_k + val_j) and is_pentagonal(val_k - val_j):
+                return min(abs(val_j - val_k), abs(val_k - val_j))
+
+if __name__ == '__main__':
+    print "Answer : %d " % (find_pair(10000))  # 10000 is just a rude guess
diff --git a/e_47.py b/e_47.py
index 1be8084..d543ff4 100644
--- a/e_47.py
+++ b/e_47.py
@@ -1,4 +1,4 @@
-#!/usr/bin/env python 
+#!/usr/bin/env python
 '''
 Created on 10 feb. 2012
 
@@ -12,19 +12,19 @@ The first two consecutive numbers to have two distinct prime factors are:
 
 The first three consecutive numbers to have three distinct prime factors are:
 
-644 = 2^2  7 * 23
+644 = 2^2 * 7 * 23
 645 = 3 * 5 * 43
 646 = 2 * 17 * 19.
 
 Find the first four consecutive integers to have four distinct primes factors. What is the first of these numbers?
-''' 
+'''
 import pickle
 
 def consecutive_primes(num):
     """
     Returns the first of the firs num consecutive primes.
     """
-    
+
 
 if __name__ == '__main__':
     print 1