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

177, 240, 1255, 630, 4487, 2040, 12249

Offset: 3

Author

Natalia Makarova, Apr 03 2011

Keywords

• nonn
• more

Comments

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.

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.

Examples

			a(7) = 4487:
    53 1277  101 1091  173 1019  773
  1013   59  863  599  881 1049   23
   179 1193  563  821  761  131  839
  1031  311  929  641  353  971  251
   443 1151  521  461  719   89 1103
  1259  233  401  683  419 1223  269
   509  263 1109  191 1181    5 1229
a(8) = 2040:
    7 499  19 487 463  67 467  31
   53 421 233 409 317 157 379  71
   61 347 239 401 313 227 373  79
  173 311 241 179 383 281 359 113
  397 151 229 127 331 269 199 337
  431 137 283 197 109 271 163 449
  439 131 353 193 101 277  89 457
  479  43 443  47  23 491  11 503
a(9) = 12249:
  1283  311 1811 2213 1571  569 2039 1163 1289
   773  653 2243 1619 2063  593 2693  383 1229
  1979 1499 2699  641  821   89  809 2003 1709
  1613 2531  101  131 2333 2441 2663  263  173
   113  179 2711  449 1361 2273   11 2543 2609
  2549 2459   59  281  389 2591 2621  191 1109
  1013  719 1913 2633 1901 2081   23 1223  743
  1493 2339   29 2129  659 1103  479 2069 1949
  1433 1559  683 2153 1151  509  911 2411 1439
		

Links

• dxdy Scientific Forum, Discussion at the scientific forum dxdy.ru (in Russian)
• Natalia Makarova, Associative magic squares of prime numbers

Crossrefs

Cf. A164843.

Extensions

a(9) from Natalia Makarova, Mar 08 2015