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%I #14 Jan 09 2021 02:12:33
%S 4,143,669,2088,8318,30885,87643
%N Minimal index of order n Stanley's antimagic square composed of Smith numbers.
%C 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.
%H <a href="http://dxdy.ru/topic58862.html">Antimagic squares</a> (in Russian), discussion at dxdy.ru
%H Carlos Rivera <a href="http://www.primepuzzles.net/puzzles/puzz_681.htm">Puzzle 681</a>
%e Examples of order n Stanley's antimagic squares with minimal index S composed of Smith numbers:
%e .
%e n=2, S=143
%e 22 58
%e 85 121
%e .
%e For n=3, S=669 we have:
%e 22 58 202
%e 85 121 265
%e 346 382 526
%e Here 22+121+526 = 22+265+382 = 58+265+346 = 58+85+526 = 202+121+346 = 202+85+382 = 669.
%e .
%e n=4, S=2088
%e 85 94 121 517
%e 346 355 382 778
%e 526 535 562 958
%e 654 663 690 1086
%e .
%e n=5, S=8318 (author V. Pavlovsky)
%e 58 121 382 562 1111
%e 202 265 526 706 1255
%e 454 517 778 958 1507
%e 1858 1921 2182 2362 2911
%e 3802 3865 4126 4306 4855
%e .
%e n=6, S=30885
%e 319 346 1642 1678 1966 3226
%e 535 562 1858 1894 2182 3442
%e 1255 1282 2578 2614 2902 4162
%e 3595 3622 4918 4954 5242 6502
%e 4279 4306 5602 5638 5926 7186
%e 13639 13666 14962 14998 15286 16546
%e .
%e n=7, S=87643 (author J. K. Andersen)
%e 454 634 1858 2614 4054 4414 16474
%e 1642 1822 3046 3802 5242 5602 17662
%e 2038 2218 3442 4198 5638 5998 18058
%e 5674 5854 7078 7834 9274 9634 21694
%e 5935 6115 7339 8095 9535 9895 21955
%e 20362 20542 21766 22522 23962 24322 36382
%e 24214 24394 25618 26374 27814 28174 40234
%Y Cf. A006753, A210710.
%K nonn,base,more
%O 1,1
%A _Natalia Makarova_, Apr 29 2013
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