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A188537 The smallest constant of an n X n associative magic square composed of distinct primes. 2
177, 240, 1255, 630, 4487, 2040, 12249 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

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.

LINKS

Table of n, a(n) for n=3..9.

dxdy Scientific Forum, Discussion at the scientific forum dxdy.ru (in Russian)

Natalia Makarova, Associative magic squares of prime numbers

EXAMPLE

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

CROSSREFS

Cf. A164843.

Sequence in context: A164843 A268790 A077786 * A169641 A255786 A147028

Adjacent sequences:  A188534 A188535 A188536 * A188538 A188539 A188540

KEYWORD

nonn,more

AUTHOR

Natalia Makarova, Apr 03 2011

EXTENSIONS

a(9) from Natalia Makarova, Mar 08 2015

STATUS

approved

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Last modified February 20 12:57 EST 2019. Contains 320327 sequences. (Running on oeis4.)