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

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The discussion centers on the confusion surrounding the decoding of a natural number back into a sequence of natural numbers, specifically in the context of Gödel numbering. Participants clarify the encoding process and emphasize the importance of understanding the specific encoding method being used. One participant suggests referring to Gödel's encoding as outlined in a Wikipedia article, highlighting that if this encoding is used, decoding can be achieved through prime factorization. This method allows for the retrieval of the original sequence from the encoded natural number.
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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,...xn>
 
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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".
 
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