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A192087 Potential magic constants of a 10 X 10 magic square composed of consecutive primes.

%I A192087 #17 Jan 09 2021 02:12:47
%S A192087 2862,3092,3500,4222,4780,5608,7124,10126,10198,11212,11426,12140,
%T A192087 12212,12284,12356,12428,12714,12854,12924,15270,16252,16476,18594,
%U A192087 18672,18750,18828,19214,20764,21150,23752,24214,24598,24828,27180,27342,27424,27916,28666,29406,29568
%N A192087 Potential magic constants of a 10 X 10 magic square composed of consecutive primes.
%C A192087 For a 10 X 10 magic square composed of 100 consecutive primes, the sum of these primes must be a multiple of 20.
%C A192087 This sequence consists of even integers equal the sum of 100 consecutive primes divided by 10. It is not known whether each such set of consecutive primes can be arranged into a 10 X 10 magic square but it looks plausible.
%C A192087 Actual magic squares were constructed for all listed magic constants <= 11212.
%H A192087 Natalia Makarova, <a href="http://www.natalimak1.narod.ru/prime10.htm">Sequence of Magic Numbers MK 10th Order</a> (in Russian).
%e A192087 a(1)=2862 for a square containing prime(9)..prime(108):
%e A192087   [23  179  409  373  263  137  461  457  523   37
%e A192087   193  353  443  199  317  109  337  397  131  383
%e A192087    71   73  389  251  593  167  439  449  233  197
%e A192087   571  293  101  229   29  557  271   31  379  401
%e A192087   127  419  283  241  269  239  547   89  181  467
%e A192087   491  433  223  113   41  577   43  311  563   67
%e A192087   281   97  163  587  191  313  149  509  421  151
%e A192087   307  499  227  431  103   83   59  479  211  463
%e A192087   277  359  257  331  569  541   53   79   47  349
%e A192087   521  157  367  107  487  139  503   61  173  347]
%e A192087 .
%e A192087 a(10)=11212
%e A192087   [769   863  1171   967   859  1381  1237  1459  1289  1217
%e A192087   1163   953   797  1297  1049  1021  1303   977  1423  1229
%e A192087    809  1277  1153   937  1151  1409  1291   839  1249  1097
%e A192087   1429  1231  1193  1451  1061   829   821  1361   823  1013
%e A192087   1453   997   947  1091  1321   887  1283   941   811  1481
%e A192087   1069  1201  1427  1129   907   919  1373  1039  1117  1031
%e A192087   1009  1123  1301  1093  1367  1483   911  1051  1087   787
%e A192087    991  1109  1279   877  1223   929  1187  1433  1327   857
%e A192087   1213  1439  1063   971  1447   883   773  1259   983  1181
%e A192087   1307  1019   881  1399   827  1471  1033   853  1103  1319]
%p A192087 s:= proc(n) option remember;
%p A192087        `if` (n=1, add (ithprime(i), i=1..100),
%p A192087                   ithprime(n+99) -ithprime(n-1) +s(n-1))
%p A192087     end:
%p A192087 a:= proc(n) option remember; local k, m;
%p A192087        a(n-1);
%p A192087        for k from 1+b(n-1) while irem (s(k), 20, 'm')<>0 do od;
%p A192087        b(n):= k; m
%p A192087     end:
%p A192087 a(0):=0: b(0):=0:
%p A192087 seq (2*a(n), n=1..50);
%Y A192087 Cf. A073520, A173981, A176571, A177434, A188536, A189188, A191679.
%K A192087 nonn
%O A192087 1,1
%A A192087 _Natalia Makarova_, Jun 23 2011