Re New Transforms

Marc LeBrun mlb at
Wed Jan 5 16:31:55 CET 2000

>= N. J. A. Sloane
>Implicit in Christian Bower's helpful comments was the notion
>that the set of all differences of a sequence is another
>transform worth including: [ALLDIFFS]

A twist on this might be to give the spectrum of pair-differences (or
whatever) of the sequence.

Then the set-sequence as defined by ALLDIFFS (or whatever) are those
indices with non-zero amplitude

That itself is also a possibly-useful transform: "n such that A[n] != 0".

(The "(or whatever)"s above can of course be replaced with other stuff, an
obvious large class of examples being the spectra defined by different
kinds of partitionings.)

Also, as you're probably aware, a possible danger of the sort of program
you included for ALLDIFFS is that it operates on finite sequences; it may
miss some small differences arising from distant pairs.  I don't know if
that matters though, for applications like superseeker.

Happy New Sequences!

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