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A191679 Potential magic constants of 9x9 magic squares composed of consecutive primes. 1
2211, 2261, 2311, 2463, 2725, 4257, 6125, 6611, 7821, 9841, 9973, 10303, 10499, 10631, 10953, 11987, 12115, 12179, 12243, 12309, 12375, 12637, 12837, 13497, 13695, 14169, 15063, 15395, 16207, 16483, 16821, 17605, 17891, 19017, 20345, 20487, 21135, 22539, 22811, 23219, 23985 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For a 9x9 magic square composed of 81 consecutive primes, it is necessary that the sum of these primes is a multiple of 9.

This sequence consists of integers equal the sum of 81 consecutive primes divides by 9. It is not known whether each such set of consecutive primes can be arranged into 9x9 magic square but it looks plausible.

LINKS

Table of n, a(n) for n=1..41.

Stefano Tognon, Squares from 37 (in Italian)

Natalia Makarova, Sequence of Magic Numbers MK 9th Order (in Russian)

EXAMPLE

a(1)= 2211 for a square containing prime(12)..prime(92):

[37 127 163 179 229 233 379 421 443

41 431 463 457 59 139 433 109 79

409 311 389 71 307 347 281 53 43

373 137 181 251 401 239 317 89 223

173 419 101 103 113 353 313 277 359

97 383 397 479 47 197 107 263 241

349 131 193 149 367 199 73 467 283

439 61 257 191 227 167 151 449 269

293 211 67 331 461 337 157 83 271]

a(2) = 2261 for a square containing prime(13)..prime(93):

[41  379  281  467  349  257  229  199  59

313  223  127  337  131  101  479  107  443

409  71  331  79  137  263  347  271  353

211  307  487  149  251  293  181  113  269

191  419  109  439  173  233  103  397  197

97  283  193  317  433  457  241  157  83

461  139  239  359  373  179  67  401  43

89  277  73  53  367  167  463  389  383

449  163  421  61  47  311  151  227  431

]

MAPLE

s:= proc(n) option remember;

       `if` (n=1, add (ithprime(i), i=1..81),

                  ithprime(n+80) -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), 9, 'm')<>0 do od;

       b(n):= k; m

    end:

a(0):=0: b(0):=0:

seq (a(n), n=1..50);

MATHEMATICA

Total[#]/9&/@Select[Partition[Prime[Range[500]], 81, 1], Divisible[ Total[ #], 9]&] (* Harvey P. Dale, Jan 08 2014 *)

CROSSREFS

Cf. A073520, A173981, A176571, A177434, A188536, A189188.

Sequence in context: A226562 A031772 A031545 * A238456 A031725 A077693

Adjacent sequences:  A191676 A191677 A191678 * A191680 A191681 A191682

KEYWORD

nonn

AUTHOR

Natalia Makarova, Jun 11 2011

EXTENSIONS

Edited by Max Alekseyev, Jun 18 2011

STATUS

approved

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Last modified June 25 11:59 EDT 2017. Contains 288710 sequences.