cp's OEIS Frontend

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

%I A225133 #14 Jan 09 2021 02:12:33
%S A225133 4,143,669,2088,8318,30885,87643
%N A225133 Minimal index of order n Stanley's antimagic square composed of Smith numbers.
%C A225133 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 A225133 <a href="http://dxdy.ru/topic58862.html">Antimagic squares</a> (in Russian), discussion at dxdy.ru
%H A225133 Carlos Rivera <a href="http://www.primepuzzles.net/puzzles/puzz_681.htm">Puzzle 681</a>
%e A225133 Examples of order n Stanley's antimagic squares with minimal index S composed of Smith numbers:
%e A225133 .
%e A225133 n=2, S=143
%e A225133   22  58
%e A225133   85 121
%e A225133 .
%e A225133 For n=3, S=669 we have:
%e A225133    22  58 202
%e A225133    85 121 265
%e A225133   346 382 526
%e A225133 Here 22+121+526 = 22+265+382 = 58+265+346 = 58+85+526 = 202+121+346 = 202+85+382 = 669.
%e A225133 .
%e A225133 n=4, S=2088
%e A225133    85  94 121 517
%e A225133   346 355 382 778
%e A225133   526 535 562 958
%e A225133   654 663 690 1086
%e A225133 .
%e A225133 n=5, S=8318 (author V. Pavlovsky)
%e A225133     58  121  382  562 1111
%e A225133    202  265  526  706 1255
%e A225133    454  517  778  958 1507
%e A225133   1858 1921 2182 2362 2911
%e A225133   3802 3865 4126 4306 4855
%e A225133 .
%e A225133 n=6, S=30885
%e A225133     319   346  1642  1678  1966  3226
%e A225133     535   562  1858  1894  2182  3442
%e A225133    1255  1282  2578  2614  2902  4162
%e A225133    3595  3622  4918  4954  5242  6502
%e A225133    4279  4306  5602  5638  5926  7186
%e A225133   13639 13666 14962 14998 15286 16546
%e A225133 .
%e A225133 n=7, S=87643 (author J. K. Andersen)
%e A225133     454   634  1858  2614  4054  4414 16474
%e A225133    1642  1822  3046  3802  5242  5602 17662
%e A225133    2038  2218  3442  4198  5638  5998 18058
%e A225133    5674  5854  7078  7834  9274  9634 21694
%e A225133    5935  6115  7339  8095  9535  9895 21955
%e A225133   20362 20542 21766 22522 23962 24322 36382
%e A225133   24214 24394 25618 26374 27814 28174 40234
%Y A225133 Cf. A006753, A210710.
%K A225133 nonn,base,more
%O A225133 1,1
%A A225133 _Natalia Makarova_, Apr 29 2013