added ability to specify starting number of digits for collatz search, and a quick and dirty test of a power of 2 algorithm.

collatz/collatzSearch.py

@@ -3,7 +3,9 @@
 import sys
 import collatz
 
-usage='usage: collatzSearch [digits] outputs the lenght of the collatz sequence for every number less than 10^digits'
+usage='usage: collatzSearch [digits] ([startDigits]) outputs the lenght of the collatz sequence for every number less than 10^digits, starting with 10^startDidgits.'
+
+nextNumber = 1
 
 if len(sys.argv)<2:
     print(usage)
@@ -15,8 +17,13 @@ try:
 except:
     print(usage)
     sys.exit()
+if len(sys.argv)>=3:
+    try:
+        nextNumber = 10**int(sys.argv[2])
+    except:
+        print(usage)
+        sys.exit()
 
-nextNumber = 1
 maxNumber = 10**digits
 
 while nextNumber<maxNumber:

collatz/collatzSequence.py

@@ -15,7 +15,9 @@ try:
 except:
     print(usage)
     sys.exit()
-
+seqLength = 0
 while number != 1:
     number = collatz.nextInSequence(number)
+    seqLength += 1
     print(number)
+print('length of '+str(seqLength))

powerOf2.py

@@ -0,0 +1,17 @@
+#! /usr/bin/env python3
+
+def slowMethod(n):
+    while (n!=1):
+        if (n%2!=0):
+            return False
+        n = n //2
+    return True
+
+def fastMethod(n):
+    return (n&(n-1))==0
+
+for n in range(1,1000000):
+    if slowMethod(n):
+        print(n)
+    if fastMethod(n):
+        print(n)