[seqfan] Dividing by a constant, policy?
rhhardin at att.net
rhhardin at att.net
Sat Apr 4 21:13:12 CEST 2009
When should a sequence be divided by a common factor, if it's an empirically computed sequence; that is, you don't know a priori whether the common factor will continue or not.
On the one hand, say you have so many terms that it seems certain that the interesting sequence is the one with the common factor removed.
The hazard of wrongly removing it is that the sequence can't be extended past the common factor failure; the hazard of not correctly removing it is that the sequence is obscured.
Suppose you wanted to automate the choice! Would it be correct to guess that if the common factor is C, that the odds of all terms being divisible by C by chance would be (1/C)^N if you have N terms? Thus you could limit the division to cases where, say, it's one in a thousand that you've divided C out wrongly. So, for example, you'd need ten terms to justify dividing by a common 2.
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rhhardin at mindspring.com
rhhardin at att.net (either)
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