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A188536 Potential magic constants of 7 X 7 magic squares composed of consecutive primes.

%I A188536 #31 Jan 20 2021 19:13:53
%S A188536 797,1077,1651,1691,1895,2059,2817,3263,4193,4615,4803,4987,5453,5501,
%T A188536 5745,5993,6427,6761,7149,7547,7797,7943,8489,8705,9439,9747,9899,
%U A188536 10201,10347,10661,11059,12367,12591,12815,13095,13861,14359,14693
%N A188536 Potential magic constants of 7 X 7 magic squares composed of consecutive primes.
%C A188536 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.
%C A188536 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.
%H A188536 Alois P. Heinz, <a href="/A188536/b188536.txt">Table of n, a(n) for n = 1..10000</a>
%H A188536 Natalia Makarova, <a href="http://www.natalimak1.narod.ru/mk7prime.htm">Order 7 magic squares, which consist of sequential primes</a> (in Russian)
%e A188536 a(2) = 1077:
%e A188536   [ 281  167  101   43  191   37  257
%e A188536     173   79  227   71  179  211  137
%e A188536     157  109  139  277   47  251   97
%e A188536     199  151   41   89  223  193  181
%e A188536      83  197  239  229  107  163   59
%e A188536      53  103  263  127  269  149  113
%e A188536     131  271   67  241   61   73  233 ]
%e A188536 .
%e A188536 a(3) = 1651:
%e A188536   [ 239  349  359  113  127  271  193
%e A188536     109  277  311  293  191  307  163
%e A188536     149  223  281  379  283  197  139
%e A188536     199  233  251  211  373  157  227
%e A188536     367  331  179  137  151  173  313
%e A188536     241  131  103  337  257  229  353
%e A188536     347  107  167  181  269  317  263 ]
%p A188536 s:= proc(n) option remember;
%p A188536        `if`(n=1, add(ithprime(i), i=1..49),
%p A188536                  ithprime(n+48) -ithprime(n-1) +s(n-1))
%p A188536     end:
%p A188536 a:= proc(n) option remember; local k, m; a(n-1);
%p A188536        for k from 1+b(n-1) while irem(s(k),7,'m')<>0 do od;
%p A188536        b(n):= k; m
%p A188536     end:
%p A188536 a(0):=0: b(0):=0:
%p A188536 seq(a(n), n=1..50);  # _Alois P. Heinz_, Apr 07 2011
%t A188536 Total[#]/7&/@Select[Partition[Prime[Range[400]],49,1], Divisible[ Total[ #],7]&]  (* _Harvey P. Dale_, Jan 03 2012 *)
%Y A188536 Cf. A173981, A176571, A177434.
%K A188536 nonn
%O A188536 1,1
%A A188536 _Natalia Makarova_, Apr 03 2011
%E A188536 Edited by _Max Alekseyev_, Jun 18 2011