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 A188536 Potential magic constants of 7 X 7 magic squares composed of consecutive primes. 4
 797, 1077, 1651, 1691, 1895, 2059, 2817, 3263, 4193, 4615, 4803, 4987, 5453, 5501, 5745, 5993, 6427, 6761, 7149, 7547, 7797, 7943, 8489, 8705, 9439, 9747, 9899, 10201, 10347, 10661, 11059, 12367, 12591, 12815, 13095, 13861, 14359, 14693 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS For a 7 X 7 magic square composed of 49 consecutive primes, it is necessary that the sum of these primes is a multiple of 7. This sequence consists of integers equal to the sum of 49 consecutive primes divided by 7. It is not known whether each such set of consecutive primes can be arranged into a 7 X 7 magic square but it looks plausible. LINKS Alois P. Heinz, Table of n, a(n) for n = 1..10000 Natalia Makarova, Order 7 magic squares, which consist of sequential primes (in Russian) EXAMPLE a(2) = 1077:   [ 281  167  101   43  191   37  257     173   79  227   71  179  211  137     157  109  139  277   47  251   97     199  151   41   89  223  193  181      83  197  239  229  107  163   59      53  103  263  127  269  149  113     131  271   67  241   61   73  233 ] . a(3) = 1651:   [ 239  349  359  113  127  271  193     109  277  311  293  191  307  163     149  223  281  379  283  197  139     199  233  251  211  373  157  227     367  331  179  137  151  173  313     241  131  103  337  257  229  353     347  107  167  181  269  317  263 ] MAPLE s:= proc(n) option remember;        `if`(n=1, add(ithprime(i), i=1..49),                  ithprime(n+48) -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), 7, 'm')<>0 do od;        b(n):= k; m     end: a(0):=0: b(0):=0: seq(a(n), n=1..50);  # Alois P. Heinz, Apr 07 2011 MATHEMATICA Total[#]/7&/@Select[Partition[Prime[Range[400]], 49, 1], Divisible[ Total[ #], 7]&]  (* Harvey P. Dale, Jan 03 2012 *) CROSSREFS Cf. A173981, A176571, A177434. Sequence in context: A336943 A108251 A108252 * A252346 A256026 A200201 Adjacent sequences:  A188533 A188534 A188535 * A188537 A188538 A188539 KEYWORD nonn AUTHOR Natalia Makarova, Apr 03 2011 EXTENSIONS Edited by Max Alekseyev, Jun 18 2011 STATUS approved

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Last modified August 10 11:03 EDT 2022. Contains 356039 sequences. (Running on oeis4.)