login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

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: 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 19 11:44 EDT 2020. Contains 337880 sequences. (Running on oeis4.)