# cilleruelo: A class of multiplicative magic squares due to Cilleruelo and... In magic: Create and Investigate Magic Squares

## Description

Cilleruelo and Luca give a class of multiplicative magic squares whose behaviour is interesting.

## Usage

 `1` ```cilleruelo(n, m) ```

## Arguments

 `n,m` Arguments: usually integers

a 4x4 array

## Value

Returns a 4x4 matrix.

## Author(s)

Robin K. S. Hankin

## References

Javier Cilleruelo and Florian Luca 2010, “On multiplicative magic squares”, The Electronic Journal of Combinatorics vol 17, \#N8

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```is.magic(cilleruelo(5,6)) is.magic(cilleruelo(5,6),func=prod) f <- function(n){ jj <- sapply( seq(from=5,len=n), function(i){cilleruelo(i,i-4)} ) xM <- apply(jj,2,max) xm <- apply(jj,2,min) cbind(xM-xm , 5^(5/12)*xm^0.5 , 6*xm^0.5) } matplot(f(200),type='l',log='xy',xlab='n',ylab='') legend(x="topleft",legend=c("xM-xm","5^(5/12).xm^(1/2)","6xm^(1/2)"), lty=1:3,col=1:3) ```

magic documentation built on Feb. 9, 2022, 1:07 a.m.