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A258082 Smallest magic constant of most-perfect magic squares of order 2n composed of distinct prime numbers.

%I A258082 #23 May 31 2015 05:59:23
%S A258082 240,29790,24024
%N A258082 Smallest magic constant of most-perfect magic squares of order 2n composed of distinct prime numbers.
%C A258082 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 A258082 All most-perfect magic squares are pandiagonal.
%C A258082 All pandiagonal magic squares of order 4 are most-perfect (cf. A191533).
%H A258082 N. Makarova, <a href="http://www.primepuzzles.net/puzzles/puzz_671.htm">Puzzle 671: Most Perfect Magic Squares</a>, Prime Puzzles & Problems.
%H A258082 Wikipedia, <a href="http://en.wikipedia.org/wiki/Most-perfect_magic_square">Most-perfect magic square</a>
%e A258082 a(3)=29790 corresponds to the following most-perfect magic square of order 6:
%e A258082    149 9161 2309 6701 2609 8861
%e A258082   9067 1483 6907 3943 6607 1783
%e A258082   4139 5171 6299 2711 6599 4871
%e A258082   3229 7321 1069 9781  769 7621
%e A258082   5987 3323 8147  863 8447 3023
%e A258082   7219 3331 5059 5791 4759 3631
%e A258082 a(4)=24024 corresponds to the following most-perfect magic square of order 8:
%e A258082     19 5923 1019 4423 4793 1277 3793 2777
%e A258082   4877 1193 3877 2693  103 5839 1103 4339
%e A258082    499 5443 1499 3943 5273  797 4273 2297
%e A258082   5297  773 4297 2273  523 5419 1523 3919
%e A258082   1213 4729 2213 3229 5987   83 4987 1583
%e A258082   5903  167 4903 1667 1129 4813 2129 3313
%e A258082    733 5209 1733 3709 5507  563 4507 2063
%e A258082   5483  587 4483 2087  709 5233 1709 3733
%Y A258082 Cf. A191533.
%K A258082 bref,nonn,more
%O A258082 2,1
%A A258082 _Natalia Makarova_, May 23 2015