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

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

Offset: 1

Author

Natalia Makarova, Apr 03 2011

Keywords

• nonn

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.

Examples

			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 ]
		

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)

Crossrefs

Cf. A173981, A176571, A177434.

Programs

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 *)

Extensions

Edited by Max Alekseyev, Jun 18 2011