smallest all-semiprime magic square

[Jonathan Post]

The Order 4 semiprime magic square is:

28213  23611  23257  27151
24319  26089  26443  28213
25735  24673  25027  26797
23965  27859  27505  22903

The magic number (row, column, diagonal sum)
= 102232 = 2^3 * 13 * 983.
By another curious "base" concidence, 13 and 983 are emirps.

These semiprime (k-almost prime) magic squares (cubes) raise new questions
of enumeration, that can yield new sequences.  If, that is, anyone is
interested.

Best,

Jonathan Vos Post

On 12/23/06, Jonathan Post <jvospost3 at gmail.com> wrote:
>
> Using A096003 and A097824,  here is the smallest all-semiprime magic
> square, which I just discovered today:
>
> ============
> 1139   635   995
>  779   923  1067
>  851  1211   707
> ============
>
> In numerical order, these entries are:
> 635 = 5*127
> 707 = 7*101
> 779 = 19*41
> 851 = 23*37
> 923 = 13*71
> 995 = 5*199
> 1067 = 11*97
> 1139 = 17*67
> 1211 = 7*173
>
> As I just noted in a submission to Prime Curios: 2769 is the sum of any
> row, column, or diagonal. Curiously, 2769 = 3 * 13 * 71, all three of which
> are primes when reversed (but that is too "base" for us here).
>
> Using A096003(16) = 28213, and A097824(16) = 354, one likewise has the
> smallest semiprime magic square of order 4.
>
> Using A096003(25) = 2012771, and A097824(25) = 9600, one likewise has the
> smallest semiprime magic square of order 5.
>
> I'm not sure if it's better to submit the finite full sequence 1139,
> 635,  995, 779,  923,  1067,
> 851,  1211,  707 for the order 3, and similarly for the order 4 and order
> 5; or give the sequence of row sums as a function of order n; or what.
>
> I don't know the order 6 or above.
>
> I also know the smallest order 3 of the 3-almost prime magic squares, and
> so forth, but these become "less" for most seqfans, I suspect.
>
> I admit to not yet having written down the smallest semiprime magic cbe,
> but the same method can be adapted...
>
> This is, new, is it not?
>
> Happy Hanukkah, Merry Christmas, etcetera,
>
> -- Jonathan Vos Post
>
>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://list.seqfan.eu/pipermail/seqfan/attachments/20061223/dfc8eab5/attachment-0003.htm>