Repeated function application in APL

Question

Given the integers p, q and n I would like to generate a vector of length n with the elements

(⌊p ÷ q) (⌊(⌊p ÷ q) ÷ q) ...

In other words I want to construct a vector where the i:th element is {⌊⍵ ÷ q} applied i times on p. How can I do that in APL?

Answer 1

This short solution works using scan \ works in all APLs that support even basic dfns (inline lambdas):

1↓{⌊⍵÷q}\(1+n)⍴p

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Note its inefficiency; it recalculates from the beginning for every term.

A more involved solution avoids recalculation by using / to iterate:

r←,p
{r,←⌊(¯1↑r)÷q}/(1+n)⍴1
1↓r

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