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I am trying to find a pattern 'encoded' into variables with superscript labels, which incidentally look much like exponents. FindSequenceFunction though doesn't seem to care about even simple patterns.

This doesn't work:

FindSequenceFunction[Table[Superscript[x,n],{n,1,6}]]

Even if it's syntactically identical to 

FindSequenceFunction[Table[Power[x,n],{n,1,6}]]

Is there way to extend FindSequenceFunction to work on indices?

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  • $\begingroup$ I think not but they’re always improving things. I think it uses (mathematical) analytic methods to determine a formula. For instance Power has special properties such as a constant ratio between successive terms. I think its algorithms are built on such analytical properties. “Holonomic” is a broad class of functions it can handle. Conceivably it could be extended to handle symbolic patterns involving non mathematical functions but I don’t think it has been. $\endgroup$
    – Michael E2
    Nov 16, 2019 at 13:31

1 Answer 1

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It certainly can if the downvalues of Superscript comprise a sequence it can deal with. Here is an example.

Clear[Superscript]
Do[Superscript[x, i] = i^2, {i, 6}];
DownValues @ Superscript

downvals

Then

FindSequenceFunction[Table[Superscript[x, n], {n, 6}]]

#1^2 &

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