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A188537 The smallest constant of an n X n associative magic square composed of distinct primes. 2

%I

%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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Last modified August 17 19:38 EDT 2022. Contains 356189 sequences. (Running on oeis4.)