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 A191679 Potential magic constants of 9 X 9 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 9 X 9 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 9 X 9 magic square but it looks plausible. LINKS 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: A031772 A305880 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 October 19 11:44 EDT 2020. Contains 337880 sequences. (Running on oeis4.)