Generating an infinite list of the hamming sequence

Question

So I have to implement a function avalanche :: [Integer] that returns a sorted, infinite list of the hamming sequence in Haskell.

• This sequence is defined as: n = 3^i ∗ 5^j ∗ 7^k for i, j, k > 0

• Or with pretty Latex:

I'm still very new to Haskell and have tried multiple things with the iterate function, like:

avalanche = sort ((iterate (\x -> 3 ^ x) 1) ++ (iterate (\x -> 5 ^ x) 1) ++ (iterate (\x -> 7 ^ x) 1))

Which doesn't work, cause it only returns the numbers for (i = j = k) > 0.

How can I write a function which uses different permutations and starts at 0?

Some expected sample-output:

ghci> take 10 avalanche
[1,3,5,7,9,15,21,25,27,35]

EDIT:

I'm unable to find an algorithm that predicts the right in-/decrementation of i, j, and k, as they seem to grow and shrink in no concise pattern.

//       n                          i j k
//       01     3^0 * 5^0 * 7^0     0 0 0
//       03     3^1 * 5^0 * 7^0     1 0 0
//       05     3^0 * 5^1 * 7^0     0 1 0
//       07     3^0 * 5^0 * 7^1     0 0 1
//       09     3^2 * 5^0 * 7^0     2 0 0
//       15     3^1 * 5^1 * 7^0     1 1 0
//       21     3^1 * 5^0 * 7^1     1 0 1
//       25     3^0 * 5^2 * 7^0     0 2 0
//       27     3^3 * 5^0 * 7^0     3 0 0
//       35     3^0 * 5^1 * 7^1     0 1 1
//       45     3^0 * 5^1 * 7^1     0 1 1
//       49     3^0 * 5^0 * 7^2     0 0 2