A258082 - OEIS

%I #23 May 31 2015 05:59:23

%S 240,29790,24024

%N Smallest magic constant of most-perfect magic squares of order 2n composed of distinct prime numbers.

%C A magic square of order 2n is most-perfect if the following two conditions hold: (i) every 2 x 2 subsquare (including wrap-around) sum to 2T; and (ii) any pair of elements at distance n along a diagonal or a skew diagonal sum to T, where T= S/n, S is the magic constant.

%C All most-perfect magic squares are pandiagonal.

%C All pandiagonal magic squares of order 4 are most-perfect (cf. A191533).

%H N. Makarova, <a href="http://www.primepuzzles.net/puzzles/puzz_671.htm">Puzzle 671: Most Perfect Magic Squares</a>, Prime Puzzles & Problems.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Most-perfect_magic_square">Most-perfect magic square</a>

%e a(3)=29790 corresponds to the following most-perfect magic square of order 6:

%e    149 9161 2309 6701 2609 8861

%e   9067 1483 6907 3943 6607 1783

%e   4139 5171 6299 2711 6599 4871

%e   3229 7321 1069 9781  769 7621

%e   5987 3323 8147  863 8447 3023

%e   7219 3331 5059 5791 4759 3631

%e a(4)=24024 corresponds to the following most-perfect magic square of order 8:

%e     19 5923 1019 4423 4793 1277 3793 2777

%e   4877 1193 3877 2693  103 5839 1103 4339

%e    499 5443 1499 3943 5273  797 4273 2297

%e   5297  773 4297 2273  523 5419 1523 3919

%e   1213 4729 2213 3229 5987   83 4987 1583

%e   5903  167 4903 1667 1129 4813 2129 3313

%e    733 5209 1733 3709 5507  563 4507 2063

%e   5483  587 4483 2087  709 5233 1709 3733

%Y Cf. A191533.

%K bref,nonn,more

%O 2,1

%A _Natalia Makarova_, May 23 2015