logstar function_the iterate of the natural logarithm_r

Question

In R, I would like to create a function that returns the smallest n such that the n-th repetition of the natural logarithm gives a value smaller than one. Ex.: fun(9182) = 3 because ln(ln(ln(9182))) = 0,793 < 1. Any suggestions will be appreciated!

Welcome to SO - could you let us know what you have tried already? — chopper, Oct 04 '13 at 20:06

score 2 · Answer 1 · answered Oct 04 '13 at 20:03

2

logstar<-function(x){if (x<1) 0 else 1 + logstar(log(x))}

answered Oct 04 '13 at 20:03

mrip

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score 2 · Answer 2 · answered Oct 04 '13 at 20:16

@mrip's answer works well for single values. If you'd like a function that works for vectors, you'll want to use ifelse() rather than if:

> logstar <- function(x){ifelse(x<1,0,1 + logstar(ifelse(x<1,x,log(x))))}

> x = c(0.5,1,100,10000,1E8)
> logstar(x)
[1] 0 1 3 3 4

The ifelse() in the recursive call to logstar() prevents log() from generating NaN in some cases.

logstar function_the iterate of the natural logarithm_r

2 Answers2