Merge pull request #5497 from Firedrake/rogerbw-challenge-147

Solutions for challenge #147

2 files changed, 92 insertions, 0 deletions

diff --git a/challenge-147/roger-bell-west/python/ch-1.py b/challenge-147/roger-bell-west/python/ch-1.py
new file mode 100755
index 0000000000..18f827e01c
--- /dev/null
+++ b/challenge-147/roger-bell-west/python/ch-1.py
@@ -0,0 +1,53 @@
+#! /usr/bin/python3
+
+import unittest
+
+from math import sqrt,floor
+from collections import deque
+
+def genprimes(mx):
+  primesh=set(range(2,4))
+  for i in range(6,mx+2,6):
+    for j in range(i-1,i+2,2):
+      if j <= mx:
+        primesh.add(j)
+  q=deque([2,3,5,7])
+  p=q.popleft()
+  mr=floor(sqrt(mx))
+  while p <= mr:
+    if p in primesh:
+      for i in range(p*p,mx+1,p):
+        primesh.discard(i)
+    if len(q) < 2:
+      q.append(q[-1]+4)
+      q.append(q[-1]+2)
+    p=q.popleft()
+  primes=list(primesh)
+  primes.sort()
+  return primes
+
+def ltruncprimes(count):
+  out=[]
+  lt=0
+  p=[str(i) for i in genprimes(500)]
+  pp=set(p)
+  for pc in p:
+    l=len(pc)
+    c=True
+    for i in range(1,l):
+      if not pc[i:l] in pp:
+        c=False
+        break
+    if c:
+      out.append(int(pc))
+      lt += 1
+      if lt >= count:
+        break
+  return out
+
+class TestLtruncprimes(unittest.TestCase):
+
+        def test_ex1(self):
+          self.assertEqual(ltruncprimes(20),[2, 3, 5, 7, 13, 17, 23, 37, 43, 47, 53, 67, 73, 83, 97, 113, 137, 167, 173, 197],'example 1')
+
+unittest.main()
diff --git a/challenge-147/roger-bell-west/python/ch-2.py b/challenge-147/roger-bell-west/python/ch-2.py
new file mode 100755
index 0000000000..b524b7e5e5
--- /dev/null
+++ b/challenge-147/roger-bell-west/python/ch-2.py
@@ -0,0 +1,39 @@
+#! /usr/bin/python3
+
+def pentagon(n):
+  return int(n*(3*n-1)/2)
+
+def pentpair():
+  fpent=[0]
+  rpent=dict()
+  mx=0
+  a=1
+  while 1:
+    while mx < a:
+      mx += 1
+      fpent.append(pentagon(mx))
+      rpent[fpent[mx]]=mx
+    for b in range(1,a):
+      d=fpent[a]-fpent[b]
+      if d in rpent:
+        s=fpent[a]+fpent[b]
+        while s > fpent[mx]:
+          mx += 1
+          fpent.append(pentagon(mx))
+          rpent[fpent[mx]]=mx
+        if s in rpent:
+          print("P({:d}) + P({:d}) = {:d} + {:d} = {:d} = P({:d})".format(
+            a, b,
+            fpent[a], fpent[b],
+            s,
+            rpent[s]))
+          print("P({:d}) - P({:d}) = {:d} - {:d} = {:d} = P({:d})".format(
+            a, b,
+            fpent[a], fpent[b],
+            d,
+            rpent[d]))
+          quit()
+    a += 1
+          
+
+pentpair()