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