Panmagic squares of order 4n, 6n+1 and 6n-1

Produce a panmagic square of order \(4n\) or \(6n\pm 1\) using a classical method

Usage

panmagic.6npm1(n)
panmagic.6np1(m)
panmagic.6nm1(m)
panmagic.4n(m)

Arguments

m

Function panmagic.6np1(m) returns a panmagic square of order \(n=6m+1\) for \(m\geq 1\), and function panmagic.6nm1(m) returns a panmagic square of order \(n=6m-1\) for \(m\geq 1\), using a classical method.

Function panmagic.4n(m) returns a magic square of order \(n=4m\)

n

Function panmagic.6npm1(n) returns a panmagic square of order \(n\) where \(n=6m\pm 1\)

Details

Function panmagic.6npm1(n) will return a square if n is not of the form \(6m\pm 1\), but it is not necessarily magic.

References

“Pandiagonal magic square.” Wikipedia, The Free Encyclopedia. Wikimedia Foundation, Inc. 13 February 2013

Author

Robin K. S. Hankin

Examples

panmagic.6np1(1)
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,]    1   13   18   23   35   40   45
#> [2,]   37   49    5   10   15   27   32
#> [3,]   24   29   41   46    2   14   19
#> [4,]   11   16   28   33   38   43    6
#> [5,]   47    3    8   20   25   30   42
#> [6,]   34   39   44    7   12   17   22
#> [7,]   21   26   31   36   48    4    9
panmagic.6npm1(13)
#>       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
#>  [1,]    1   25   36   47   58   69   80  104  115   126   137   148   159
#>  [2,]  145  169   11   22   33   44   55   66   90   101   112   123   134
#>  [3,]  120  131  155  166    8   19   30   41   65    76    87    98   109
#>  [4,]   95  106  130  141  152  163    5   16   27    51    62    73    84
#>  [5,]   70   81   92  116  127  138  149  160    2    26    37    48    59
#>  [6,]   45   56   67   91  102  113  124  135  146   157    12    23    34
#>  [7,]   20   31   42   53   77   88   99  110  121   132   156   167     9
#>  [8,]  164    6   17   28   52   63   74   85   96   107   118   142   153
#>  [9,]  139  150  161    3   14   38   49   60   71    82    93   117   128
#> [10,]  114  125  136  147  158   13   24   35   46    57    68    79   103
#> [11,]   89  100  111  122  133  144  168   10   21    32    43    54    78
#> [12,]   64   75   86   97  108  119  143  154  165     7    18    29    40
#> [13,]   39   50   61   72   83   94  105  129  140   151   162     4    15

all(sapply(panmagic.6np1(1:3),is.panmagic))
#> [1] TRUE