How to Decode a Natural Number Back into a Sequence Using Gödel Numbering?

[atrus_ovis]

I'm ok with encoding, but I m confused about decoding a natural number back into a sequence of natural numbers.

For example, to decode a natural number N back to the sequence <x₁,x₂,...x_n>

 

[Coin]

How about you explain to us how you are going about encoding the sequence into a natural number, and then we can help figure out how to do the reverse? As I understand there is more than one system you could call a "godel numbering".

Is this the encoding you are using?

http://en.wikipedia.org/wiki/Gödel_numbering#G.C3.B6del.27s_encoding

If it is, then the process for decode is simply "Perform a prime factorization".