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