[seqfan] Re: Dividing by a constant, policy?
Maximilian Hasler
maximilian.hasler at gmail.com
Sun Apr 5 01:09:17 CEST 2009
Maybe you should submit both: the "original" sequence which is in some
sense the "natural" version but includes the common(?) factor, and the
"reduced" one with an adequate comment and "careful" definition, e.g.
"b(n) = a(n) / g, nearest integer if fraction; comment : it appears
that all terms a(n) are multiple of g, but this has not yet been
proved."
(Actually, the "nearest integer" part might be omitted from the %N
(definition) of the sequence (and maybe remain in a comment) ; if it
becomes necessary, the title can be corrected.)
There are several examples (cf. divisibility sequences recently listed
by RKG) where a common factor is perfectly known, but still it remains
in the sequence.
Maximilian
On Sat, Apr 4, 2009 at 3:13 PM, <rhhardin at att.net> wrote:
> 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.
>
>
> --
> rhhardin at mindspring.com
> rhhardin at att.net (either)
>
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