It shouldn't be too hard to make this work.

By simply looking at the sequence of the pair-wise difference and ratio and correlating them to the original sequence or a constant, you can get good guesses for most commonly used sequences, if you just allow a few levels of recursion: 

1, 2, 3, 4, 5
   differences 1, 1, 1, 1 # constant
1, 2, 4, 8, 16
   ratios:     2, 2, 2, 2 # constant
1, 2, 3, 5, 8
   differences: 1, 2, 3, 5 # sames as original  shifted by one
1, 11, 111, 1111, 11111
   differences: 10, 100, 1000, 10000
       ratios: 10, 10, 10 # constant

[download]

The fibonacci sequence is the only one example that needs autocorrelating. Other ones that could use the autocorrelation are -1, 1, -1, 1, ... and 0, 1, 0, 1, ....

In case of ambiguousness the solution with the shallowest recursion would win.

I'll try to come up with a prototype implementation that can be used as basis for a specification. But it won't be this or the next week, so have a little patience ;)

Ideally there would be some sub or method that can be overridden to detect sequences if the built-in mechanism fails..

In reply to Re^3: Numerically generate the perl sequence 1, 11, 111, .... by moritz
in thread Generate the perl sequence 1, 11, 111, .... by alih110

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