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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??


in reply to Re^2: Numerically generate the perl sequence 1, 11, 111, ....
in thread 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

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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