R: A class of multiplicative magic squares due to Cilleruelo and...

cilleruelo {magic} | R Documentation

## A class of multiplicative magic squares due to Cilleruelo and Luca

### Description

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

### Usage

    cilleruelo(n, m)

### Arguments

`n,m` | Arguments: usually integers

### Details

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

    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)

[Package magic version 1.5-8 Index]