Re^3: Numerically generate the perl sequence 1, 11, 111, ....

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..

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Re^4: Numerically generate the perl sequence 1, 11, 111, .... by JavaFan (Canon) on Oct 12, 2008 at 15:41 UTC
One interesting and useful sequence that springs to mind is: `2, 3, 5, 7, 11, 13, ... # Prime numbers.` [download] but with neither differences, nor ratios could one continue the sequence.	[reply] [d/l]
Re^5: Numerically generate the perl sequence 1, 11, 111, .... by moritz (Cardinal) on Oct 12, 2008 at 16:07 UTC
... nor can it be efficiently computed, which is why I'd leave it out.	[reply]