As a follow-up to OT: Finding Factor Closest To Square Root and Generating powerset with progressive ordering, I started thinking about the problem: how do you generate the series of numbers composed of a given list of prime factors, where each can be used an unlimited number of times? For example, the factors 2, 3,and 5 produce the infinite list (1,2,3,4,5,6,8,9,10,12...) This is known as the generalized Hamming sequence problem.

I found on the net an elegant solution in Haskell: 

{- Merge two sorted lists -}
merge (x:xs) (y:ys)
  | x < y = x: merge xs (y:ys)
  | x > y = y: merge (x:xs) ys
  | x == y = x: merge xs ys

merge [] ys = ys
merge xs [] = xs

{-- Generic Hamming sequence on a list of factors. --}
genHam :: [Integer]->[Integer]
genHam [] = []
genHam (x:xs) = out
 where
   out = merge ( 1: map (*x) out) (genHam xs)

{- Usage:
take 10 (genHam [2,3,5])
-}

[download]
The challenge would be to do this in perl. I believe perl6 has or will soon be getting Haskell-like lazy infinite lists. Can it be done in perl5?

In reply to Hamming Sequences and Lazy Lists by tall_man

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