cp's OEIS Frontend

A191679 Potential magic constants of 9 X 9 magic squares composed of consecutive primes.

%I A191679 #28 Oct 28 2019 04:20:51
%S A191679 2211,2261,2311,2463,2725,4257,6125,6611,7821,9841,9973,10303,10499,
%T A191679 10631,10953,11987,12115,12179,12243,12309,12375,12637,12837,13497,
%U A191679 13695,14169,15063,15395,16207,16483,16821,17605,17891,19017,20345,20487,21135,22539,22811,23219,23985
%N A191679 Potential magic constants of 9 X 9 magic squares composed of consecutive primes.
%C A191679 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.
%C A191679 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.
%H A191679 Stefano Tognon, <a href="http://digilander.libero.it/ice00/magic/prime/squares37.html#9">Squares from 37</a> (in Italian).
%H A191679 Natalia Makarova, <a href="http://www.natalimak1.narod.ru/prime9.htm">Sequence of Magic Numbers MK 9th Order</a> (in Russian).
%e A191679 a(1)=2211 for a square containing prime(12)..prime(92):
%e A191679   [37 127 163 179 229 233 379 421 443
%e A191679    41 431 463 457  59 139 433 109  79
%e A191679   409 311 389  71 307 347 281  53  43
%e A191679   373 137 181 251 401 239 317  89 223
%e A191679   173 419 101 103 113 353 313 277 359
%e A191679    97 383 397 479  47 197 107 263 241
%e A191679   349 131 193 149 367 199  73 467 283
%e A191679   439  61 257 191 227 167 151 449 269
%e A191679   293 211  67 331 461 337 157  83 271]
%e A191679 a(2)=2261 for a square containing prime(13)..prime(93):
%e A191679   [41  379  281  467  349  257  229  199   59
%e A191679   313  223  127  337  131  101  479  107  443
%e A191679   409   71  331   79  137  263  347  271  353
%e A191679   211  307  487  149  251  293  181  113  269
%e A191679   191  419  109  439  173  233  103  397  197
%e A191679    97  283  193  317  433  457  241  157   83
%e A191679   461  139  239  359  373  179   67  401   43
%e A191679    89  277   73   53  367  167  463  389  383
%e A191679   449  163  421   61   47  311  151  227  431]
%p A191679 s:= proc(n) option remember;
%p A191679        `if` (n=1, add (ithprime(i), i=1..81),
%p A191679                   ithprime(n+80) -ithprime(n-1) +s(n-1))
%p A191679     end:
%p A191679 a:= proc(n) option remember; local k, m;
%p A191679        a(n-1);
%p A191679        for k from 1+b(n-1) while irem (s(k), 9, 'm')<>0 do od;
%p A191679        b(n):= k; m
%p A191679     end:
%p A191679 a(0):=0: b(0):=0:
%p A191679 seq (a(n), n=1..50);
%t A191679 Total[#]/9&/@Select[Partition[Prime[Range[500]],81,1],Divisible[ Total[ #],9]&] (* _Harvey P. Dale_, Jan 08 2014 *)
%Y A191679 Cf. A073520, A173981, A176571, A177434, A188536, A189188.
%K A191679 nonn
%O A191679 1,1
%A A191679 _Natalia Makarova_, Jun 11 2011
%E A191679 Edited by _Max Alekseyev_, Jun 18 2011