from itertools import tee, chain, islice, groupby
from heapq import merge
def hamming_numbers():
# 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.
def deferred_output():
'Works like a forward reference to the "output" global variable'
for i in output:
yield i
result, p2, p3, p5 = tee(deferred_output(), 4) # split the output streams
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 starting point
output = (k for k, v in groupby(combined)) # eliminate duplicates
return result
if __name__ == '__main__':
print(list(islice(hamming_numbers(), 1000))) # Show first 1000 hamming numbers
