[seqfan] Negative shifts in Plot 2 to show growth rates?

Hugo Pfoertner yae9911 at gmail.com
Fri Apr 28 18:51:46 CEST 2023


Dear SeqFans,

A little-known application of Plot2 is the graphical representation of
growth rates, i.e., usually the quotient a(n)/a(n-1) as a function of
increasing n. This type of plot is particularly desirable when the growth
rate tends towards a constant limit. With Plot2, for example, this can be
done in the following form
https://oeis.org/plot2a?name1=A275544&name2=A275544&tform1=untransformed&tform2=untransformed&shift=-1&radiop1=ratio&drawpoints=true
by specifying the third option "Plot Seq1(n)/Seq2(n+shift) vs n" and
specifying a shift for sequence 2.

Unfortunately, with the current version of Plot 2, a negative shift is
ignored. With this, only the unintuitive quotient a(n-1)/a(n) can be drawn,
which is the inverse growth rate.

Actually we want to see the limit a(n)/a(n-1) of about 1.869... to compare
it with the conjecturally same limit for A208127.

Of course, I can also create such a plot with an external program, e.g.
gnuplot, but the built-in function would have the advantage that the plot
is created with the most recent data and thus also reflects future
extensions, e.g. in the b-files.

Is there a possibility to also consider negative values for the shift?
I know that such changes have practically never been implemented, because a
collapse of the apparently almost unmaintainable function is feared, but it
doesn't hurt to ask again.

Best regards
Hugo Pfoertner


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