add collatz

Author: mgold

collatz.py

@@ -0,0 +1,39 @@
+"""
+This module, collatz.py, includes methods to work with the collatz or 3n+1
+conjecture. It contains three functions: collatz, dictionary, and orbit. More
+information is available in the docstrings of these fucntions.
+"""
+
+def collatz(n):
+  "If n is even, return n/2. If n is odd, return 3n+1."
+  if n%2:
+    return 3*n+1
+  else: 
+    return n/2
+
+def dictionary(maxval):
+  """Returns a tuple: a dictionary of numbers 1 to maxval as keys and their
+  orbits as values, and the key of the highest value."""
+  dict = {1:0}
+  highest = 1
+  for i in range(1, maxval+1):
+    j = i
+    steps = 0
+    while True: #rely on break to exit loop
+      if j not in dict:
+        j = collatz(j)
+        steps += 1
+      else:
+        dict[i] = dict[j] + steps
+        if dict[i] > dict[highest]:
+          highest = i
+        break
+  return dict, highest
+
+def orbit(n):
+  "Returns the number of steps for n to converge to 1."
+  steps = 0
+  while(n > 1):
+    n = collatz(n)
+    steps += 1
+  return steps

nthPrime.py

@@ -0,0 +1,18 @@
+import math
+
+def nthPrime(n):
+  primes = [2]
+  unchecked = 3
+  while (len(primes) < n):
+    couldBePrime = True
+    threshold = math.ceil(math.sqrt(unchecked))
+    for p in primes:
+      if not unchecked%p: #if p divides unchecked
+        couldBePrime = False #then it isn't prime
+        break
+      if p > threshold:
+       break
+    if couldBePrime:
+      primes.append(unchecked)
+    unchecked += 2
+  return primes[n-1]