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A188537 The smallest constant of an n X n associative magic square composed of distinct primes.

%I A188537 #35 Dec 15 2015 06:14:43
%S A188537 177,240,1255,630,4487,2040,12249
%N A188537 The smallest constant of an n X n associative magic square composed of distinct primes.
%C A188537 In the associative magic square the sums of every pair of elements which are center-symmetrical are equal. Associative squares exist for every magic square order.
%C A188537 a(10) <= 4950, a(11) = 26521, a(12)=8820, a(13)<=50453, a(14)=16170, a(15)=74595, a(16)<=25200, a(17)=128197, a(18)=35910, a(19)<=193363, a(20)=54600.
%H A188537 dxdy Scientific Forum, <a href="http://dxdy.ru/post425089.html#p425089">Discussion at the scientific forum dxdy.ru</a> (in Russian)
%H A188537 Natalia Makarova, <a href="/A188537/a188537.txt">Associative magic squares of prime numbers</a>
%e A188537 a(7) = 4487:
%e A188537     53 1277  101 1091  173 1019  773
%e A188537   1013   59  863  599  881 1049   23
%e A188537    179 1193  563  821  761  131  839
%e A188537   1031  311  929  641  353  971  251
%e A188537    443 1151  521  461  719   89 1103
%e A188537   1259  233  401  683  419 1223  269
%e A188537    509  263 1109  191 1181    5 1229
%e A188537 a(8) = 2040:
%e A188537     7 499  19 487 463  67 467  31
%e A188537    53 421 233 409 317 157 379  71
%e A188537    61 347 239 401 313 227 373  79
%e A188537   173 311 241 179 383 281 359 113
%e A188537   397 151 229 127 331 269 199 337
%e A188537   431 137 283 197 109 271 163 449
%e A188537   439 131 353 193 101 277  89 457
%e A188537   479  43 443  47  23 491  11 503
%e A188537 a(9) = 12249:
%e A188537   1283  311 1811 2213 1571  569 2039 1163 1289
%e A188537    773  653 2243 1619 2063  593 2693  383 1229
%e A188537   1979 1499 2699  641  821   89  809 2003 1709
%e A188537   1613 2531  101  131 2333 2441 2663  263  173
%e A188537    113  179 2711  449 1361 2273   11 2543 2609
%e A188537   2549 2459   59  281  389 2591 2621  191 1109
%e A188537   1013  719 1913 2633 1901 2081   23 1223  743
%e A188537   1493 2339   29 2129  659 1103  479 2069 1949
%e A188537   1433 1559  683 2153 1151  509  911 2411 1439
%Y A188537 Cf. A164843.
%K A188537 nonn,more
%O A188537 3,1
%A A188537 _Natalia Makarova_, Apr 03 2011
%E A188537 a(9) from _Natalia Makarova_, Mar 08 2015