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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 7x7 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 the sum of 49 consecutive primes divides by 7. It is not known whether each such set of consecutive primes can be arranged into a 7x7 magic square but it looks plausible.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

N. 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: A086393 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 March 27 04:08 EDT 2017. Contains 284144 sequences.