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A257316 Smallest magic constant of ultramagic squares of order n composed of distinct prime numbers.

%I A257316 #38 Jun 03 2024 09:44:49
%S A257316 3505,990,4613,2040
%N A257316 Smallest magic constant of ultramagic squares of order n composed of distinct prime numbers.
%C A257316 A magic square is associative if the sum of any two elements symmetric about its center is the same. A magic square is pandiagonal if the sum of the numbers in any broken diagonal equals the magic constant. A magic square is ultramagic if it is associative and pandiagonal.
%C A257316 Ultramagic squares exist for orders n>=5.
%C A257316 The following bounds for the next terms are known: 12249<=a(9)<=13059, 4200<=a(10)<=46150, a(11)>=26521, a(12)>=8820, a(13)>=49439, a(14)>=16170, a(15)>=74595, a(16)>=21840.
%H A257316 Discussion at the scientific forum dxdy.ru, <a href="http://dxdy.ru/post1002869.html#p1002869">Devilish magic squares of primes</a> (in Russian)
%H A257316 Wikipedia, <a href="http://en.wikipedia.org/wiki/Magic_square">Magic Square</a>
%e A257316 a(6)=990 corresponds to the following ultramagic square found by _Max Alekseyev_:
%e A257316   103  59 163 233 139 293
%e A257316   229 257 307 131  13  53
%e A257316   283  17  67 173 181 269
%e A257316    61 149 157 263 313  47
%e A257316   277 317 199  23  73 101
%e A257316    37 191  97 167 271 227
%e A257316 a(7)=4613 corresponds to the following ultramagic square found by _Natalia Makarova_:
%e A257316    227  617  677  431 1217 1307  137
%e A257316   1259  827 1061  509  521  167  269
%e A257316    347  929 1187   17  557  719  857
%e A257316     89  479   29  659 1289  839 1229
%e A257316    461  599  761 1301  131  389  971
%e A257316   1049 1151  797  809  257  491   59
%e A257316   1181   11  101  887  641  701 1091
%e A257316 a(8)=2040 corresponds to the following ultramagic square found by _Natalia Makarova_:
%e A257316   241 199 409 467  47  79 359 239
%e A257316   421 137   7  53 487 179 317 439
%e A257316    31 281 347 353 227 277 127 397
%e A257316   449 197 109 379 491 337  11  67
%e A257316   443 499 173  19 131 401 313  61
%e A257316   113 383 233 283 157 163 229 479
%e A257316    71 193 331  23 457 503 373  89
%e A257316   271 151 431 463  43 101 311 269
%Y A257316 Cf. A006052, A081262, A081263.
%K A257316 nonn,more
%O A257316 5,1
%A A257316 _Natalia Makarova_, Apr 20 2015