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

by moritz (Cardinal)
 on Oct 12, 2008 at 14:48 UTC ( #716680=note: print w/replies, xml ) Need Help??

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

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.
but with neither differences, nor ratios could one continue the sequence.
... nor can it be efficiently computed, which is why I'd leave it out.

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