Issue 9816:  Random.jumpahead(n) didn't work well for small values of n.
diff --git a/Lib/random.py b/Lib/random.py
index f919718..01e1420 100644
--- a/Lib/random.py
+++ b/Lib/random.py
@@ -46,6 +46,7 @@
 from math import sqrt as _sqrt, acos as _acos, cos as _cos, sin as _sin
 from os import urandom as _urandom
 from binascii import hexlify as _hexlify
+import hashlib as _hashlib
 
 __all__ = ["Random","seed","random","uniform","randint","choice","sample",
            "randrange","shuffle","normalvariate","lognormvariate",
@@ -141,6 +142,18 @@
                              "Random.setstate() of version %s" %
                              (version, self.VERSION))
 
+    def jumpahead(self, n):
+        """Change the internal state to one that is likely far away
+        from the current state.  This method will not be in Py3.x,
+        so it is better to simply reseed.
+        """
+        # The super.jumpahead() method uses shuffling to change state,
+        # so it needs a large and "interesting" n to work with.  Here,
+        # we use hashing to create a large n for the shuffle.
+        s = repr(n) + repr(self.getstate())
+        n = int(_hashlib.new('sha512', s).hexdigest(), 16)
+        super(Random, self).jumpahead(n)
+
 ## ---- Methods below this point do not need to be overridden when
 ## ---- subclassing for the purpose of using a different core generator.
 
diff --git a/Lib/test/test_random.py b/Lib/test/test_random.py
index 94c20ce..df82990 100644
--- a/Lib/test/test_random.py
+++ b/Lib/test/test_random.py
@@ -55,8 +55,6 @@
 
         with test_support.check_py3k_warnings(quiet=True):
             self.assertRaises(TypeError, self.gen.jumpahead)  # needs an arg
-            self.assertRaises(TypeError, self.gen.jumpahead, "ick")  # wrong type
-            self.assertRaises(TypeError, self.gen.jumpahead, 2.3)  # wrong type
             self.assertRaises(TypeError, self.gen.jumpahead, 2, 3)  # too many
 
     def test_sample(self):
diff --git a/Misc/NEWS b/Misc/NEWS
index e509895..13cec41 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -43,6 +43,10 @@
 Library
 -------
 
+- Issue #9816: random.Random.jumpahead(n) did not produce a sufficiently
+  different internal state for small values of n.  Fixed by salting the 
+  value.
+
 - Issue #9792: In case of connection failure, socket.create_connection()
   would swallow the exception and raise a new one, making it impossible
   to fetch the original errno, or to filter timeout errors.  Now the