A225133 Minimal index of order n Stanley's antimagic square composed of Smith numbers.

4, 143, 669, 2088, 8318, 30885, 87643

Offset: 1

Author

Natalia Makarova, Apr 29 2013

Keywords

• nonn
• base
• more

Comments

Stanley antimagic square of index d and order n is an n X n matrix where the sum of any n matrix elements in pairwise distinct rows and pairwise distinct columns equals d.

Examples

			Examples of order n Stanley's antimagic squares with minimal index S composed of Smith numbers:
.
n=2, S=143
  22  58
  85 121
.
For n=3, S=669 we have:
   22  58 202
   85 121 265
  346 382 526
Here 22+121+526 = 22+265+382 = 58+265+346 = 58+85+526 = 202+121+346 = 202+85+382 = 669.
.
n=4, S=2088
   85  94 121 517
  346 355 382 778
  526 535 562 958
  654 663 690 1086
.
n=5, S=8318 (author V. Pavlovsky)
    58  121  382  562 1111
   202  265  526  706 1255
   454  517  778  958 1507
  1858 1921 2182 2362 2911
  3802 3865 4126 4306 4855
.
n=6, S=30885
    319   346  1642  1678  1966  3226
    535   562  1858  1894  2182  3442
   1255  1282  2578  2614  2902  4162
   3595  3622  4918  4954  5242  6502
   4279  4306  5602  5638  5926  7186
  13639 13666 14962 14998 15286 16546
.
n=7, S=87643 (author J. K. Andersen)
    454   634  1858  2614  4054  4414 16474
   1642  1822  3046  3802  5242  5602 17662
   2038  2218  3442  4198  5638  5998 18058
   5674  5854  7078  7834  9274  9634 21694
   5935  6115  7339  8095  9535  9895 21955
  20362 20542 21766 22522 23962 24322 36382
  24214 24394 25618 26374 27814 28174 40234
		

Links

• Antimagic squares (in Russian), discussion at dxdy.ru
• Carlos Rivera Puzzle 681

Crossrefs

Cf. A006753, A210710.