June 2018 Update

Task/Hamming-numbers/Python/hamming-numbers-4.py

@@ -1,13 +1,25 @@
+from itertools import tee, chain, groupby, islice
 from heapq import merge
-from itertools import tee
 
-def hamming_numbers():
-    last = 1
-    yield last
+def raymonds_hamming():
+    # Generate "5-smooth" numbers, also called "Hamming numbers"
+    # or "Regular numbers".  See: http://en.wikipedia.org/wiki/Regular_number
+    # Finds solutions to 2**i * 3**j * 5**k  for some integers i, j, and k.
 
-    a,b,c = tee(hamming_numbers(), 3)
+    def deferred_output():
+        for i in output:
+            yield i
 
-    for n in merge((2*i for i in a), (3*i for i in b), (5*i for i in c)):
-        if n != last:
-            yield n
-            last = n
+    result, p2, p3, p5 = tee(deferred_output(), 4)
+    m2 = (2*x for x in p2)                          # multiples of 2
+    m3 = (3*x for x in p3)                          # multiples of 3
+    m5 = (5*x for x in p5)                          # multiples of 5
+    merged = merge(m2, m3, m5)
+    combined = chain([1], merged)                   # prepend a starting point
+    output = (k for k,g in groupby(combined))       # eliminate duplicates
+
+    return result
+
+print list(islice(raymonds_hamming(), 20))
+print islice(raymonds_hamming(), 1689, 1690).next()
+print islice(raymonds_hamming(), 999999, 1000000).next()