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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.)