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A189188 Potential magic constants of 8x8 magic squares composed of consecutive primes. 2
2016, 2244, 2336, 2570, 2762, 4106, 4362, 4464, 4566, 4670, 4776, 4934, 5952, 6870, 7036, 7146, 7588, 7644, 7700, 8824, 9756, 9930, 9988, 10394, 10454, 10514, 10690, 10868, 10928, 11560, 12620, 12682, 14986, 15424, 15808, 16000, 16510, 18668, 20434 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For a 8x8 magic square composed of 64 consecutive primes, it is necessary that the sum of these primes is a multiple of 16.

This sequence consists of even integers equal the sum of 64 consecutive primes divides by 8. It is not known whether each such set of consecutive primes can be arranged into a 8x8 magic square but it looks plausible.

LINKS

Table of n, a(n) for n=1..39.

N. Makarova Magic squares of order 8 which consist of consecutive primes (in Russian)

EXAMPLE

a(1) = 2016

[79 137 197 199 277 347 349 431

127 193 131 419 337 421 107 281

103 379 283 389 293 227 179 163

397 251 83 271 269 157 439 149

409 211 383 191 181 101 401 139

307 239 317 167 89 367 97 433

353 233 359 151 257 223 331 109

241 373 263 229 313 173 113 311]

a(12) = 4934

[823 619 461 457 631 587 599 757

443 563 647 509 733 761 787 491

503 809 419 701 661 797 487 557

683 499 743 677 449 607 617 659

439 727 571 577 719 821 601 479

811 641 593 523 421 467 709 769

691 433 673 751 773 431 613 569

541 643 827 739 547 463 521 653]

MAPLE

s:= proc(n) option remember;

       `if` (n=1, add (ithprime(i), i=1..64),

                  ithprime(n+63) -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), 16, 'm')<>0 do od;

       b(n):= k; m

    end:

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

seq (2*a(n), n=1..50);

CROSSREFS

Cf. A073520, A173981, A176571, A177434, A188536

Sequence in context: A250836 A076666 A323470 * A076582 A323749 A323469

Adjacent sequences:  A189185 A189186 A189187 * A189189 A189190 A189191

KEYWORD

nonn

AUTHOR

Natalia Makarova, Apr 18 2011

EXTENSIONS

Edited by Max Alekseyev, Jun 18 2011

STATUS

approved

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Last modified June 26 20:37 EDT 2019. Contains 324380 sequences. (Running on oeis4.)