Problem 292. Infernal Recursion

Matt Fig

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Consider the recursion relation:

x_n = (x_(n-1)*x_(n-2))^k

Given x_1, x_2, and k, x_n can be found by this definition. Write a function which takes as input arguments x_1, x_2, n and k. The output should be x_n.

For example, if x_1=exp(1), x_2=pi, n=5, and k=5/9 then:

R = get_recurse(exp(1),pi,5,4/9)

R =
      2.31187497992966

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Last Solution submitted on Apr 14, 2026

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@bmtran (Bryant Tran) on 9 Feb 2012

is there a story as to why this is "infernal"?

Matt Fig on 9 Feb 2012

I hate recursion, so it is all infernal to me! Iteration is the way to go...

David Young on 29 Feb 2012

Test suite could helpfully include n=1 and n=2 tests. I thought that it needed extra complexity to handle these, but @bmtran's top solution shows it doesn't.

Aurelien Queffurust on 12 Jun 2012

I spend a lot of time to get the correct R from the example. The issue is that you say k = 5/9 instead of 4/9 . Just a typo to correct . Thanks

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