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A192087 Potential magic constants of a 10x10 magic square composed of consecutive primes. 0
2862, 3092, 3500, 4222, 4780, 5608, 7124, 10126, 10198, 11212, 11426, 12140, 12212, 12284, 12356, 12428, 12714, 12854, 12924, 15270, 16252, 16476, 18594, 18672, 18750, 18828, 19214, 20764, 21150, 23752, 24214, 24598, 24828, 27180, 27342, 27424, 27916, 28666, 29406, 29568 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For a 10x10 magic square composed of 100 consecutive primes, it is necessary that the sum of these primes is a multiple of 20.

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 10x10 magic square but it looks plausible.

Actual magic squares were constructed for all listed magic constants <= 11212.

LINKS

Table of n, a(n) for n=1..40.

N.Makarova, Sequence of Magic Numbers MK 10th Order (in Russian)

EXAMPLE

a(1)=2862 for a square containing prime (9)..prime(108):

[23  179  409  373  263  137  461  457  523  37

193  353  443  199  317  109  337  397  131  383

71  73  389  251  593  167  439  449  233  197

571  293  101  229  29  557  271  31  379  401

127  419  283  241  269  239  547  89  181  467

491  433  223  113  41  577  43  311  563  67

281  97  163  587  191  313  149  509  421  151

307  499  227  431  103  83  59  479  211  463

277  359  257  331  569  541  53  79  47  349

521  157  367  107  487  139  503  61  173  347]

a(10)=11212

[769  863  1171  967  859  1381  1237  1459  1289  1217

1163  953  797  1297  1049  1021  1303  977  1423  1229

809  1277  1153  937  1151  1409  1291  839  1249  1097

1429  1231  1193  1451  1061  829  821  1361  823  1013

1453  997  947  1091  1321  887  1283  941  811  1481

1069  1201  1427  1129  907  919  1373  1039  1117  1031

1009  1123  1301  1093  1367  1483  911  1051  1087  787

991  1109  1279  877  1223  929  1187  1433  1327  857

1213  1439  1063  971  1447  883  773  1259  983  1181

1307  1019  881  1399  827  1471  1033  853  1103  1319]

MAPLE

s:= proc(n) option remember;

       `if` (n=1, add (ithprime(i), i=1..100),

                  ithprime(n+99) -ithprime(n-1) +s(n-1))

    end:

a:= proc(n) option remember; local k, m;

       a(n-1);

       for k from 1+b(n-1) while irem (s(k), 20, 'm')<>0 do od;

       b(n):= k; m

    end:

a(0):=0: b(0):=0:

seq (2*a(n), n=1..50);

CROSSREFS

Cf. A073520, A173981, A176571, A177434, A188536, A189188, A191679

Sequence in context: A031603 A236586 A233379 * A286007 A235960 A235571

Adjacent sequences:  A192084 A192085 A192086 * A192088 A192089 A192090

KEYWORD

nonn

AUTHOR

Natalia Makarova, Jun 23 2011

STATUS

approved

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Last modified March 24 14:04 EDT 2019. Contains 321448 sequences. (Running on oeis4.)