OFFSET
5,1
COMMENTS
A magic square is associative if the sum of any two elements symmetric about its center is the same. A magic square is pandiagonal if the sum of the numbers in any broken diagonal equals the magic constant. A magic square is ultramagic if it is associative and pandiagonal.
Ultramagic squares exist for orders n>=5.
The following bounds for the next terms are known: 12249<=a(9)<=13059, 4200<=a(10)<=46150, a(11)>=26521, a(12)>=8820, a(13)>=49439, a(14)>=16170, a(15)>=74595, a(16)>=21840.
LINKS
Discussion at the scientific forum dxdy.ru, Devilish magic squares of primes (in Russian)
Wikipedia, Magic Square
EXAMPLE
a(6)=990 corresponds to the following ultramagic square found by Max Alekseyev:
103 59 163 233 139 293
229 257 307 131 13 53
283 17 67 173 181 269
61 149 157 263 313 47
277 317 199 23 73 101
37 191 97 167 271 227
a(7)=4613 corresponds to the following ultramagic square found by Natalia Makarova:
227 617 677 431 1217 1307 137
1259 827 1061 509 521 167 269
347 929 1187 17 557 719 857
89 479 29 659 1289 839 1229
461 599 761 1301 131 389 971
1049 1151 797 809 257 491 59
1181 11 101 887 641 701 1091
a(8)=2040 corresponds to the following ultramagic square found by Natalia Makarova:
241 199 409 467 47 79 359 239
421 137 7 53 487 179 317 439
31 281 347 353 227 277 127 397
449 197 109 379 491 337 11 67
443 499 173 19 131 401 313 61
113 383 233 283 157 163 229 479
71 193 331 23 457 503 373 89
271 151 431 463 43 101 311 269
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Natalia Makarova, Apr 20 2015
STATUS
approved