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A259733 The magic constants of most-perfect magic squares of order 8 composed of distinct prime numbers. 2
24024, 26040, 43680, 44352, 44520, 44880 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
A magic square of order n = 2k is most-perfect if the following two conditions hold: (i) every 2 X 2 subsquare (including wrap-around) sums to 2T; and (ii) any pair of elements at distance k along a diagonal or a skew diagonal sums to T, where T = S/k, S is the magic constant.
All most-perfect magic squares are pandiagonal.
All pandiagonal magic squares of order 4 are most-perfect, see A191533.
The magic constants of most-perfect magic squares of order 6 composed of distinct primes see A258755.
The minimal magic constant of most-perfect magic square of order 8 composed of distinct primes corresponds to a(1) = 24024, see A258082.
It seems that only the first term, or possibly the first two terms, have been proved to be correct. The other terms are conjectural (that is, there may be missing terms). - N. J. A. Sloane, Jul 28 2015
LINKS
N. Makarova and others, Magic squares, discussion at the scientific forum dxdy.ru (in Russian), Feb. 2015.
N. Makarova, Puzzle 671: Most Perfect Magic Squares, Prime Puzzles & Problems.
EXAMPLE
a(2) = 26040 corresponds to the following most-perfect magic square by N. Makarova:
61 6229 661 5563 2087 4643 1487 5309
3719 3011 3119 3677 1693 4597 2293 3931
1777 4513 2377 3847 3803 2927 3203 3593
4139 2591 3539 3257 2113 4177 2713 3511
4423 1867 5023 1201 6449 281 5849 947
4817 1913 4217 2579 2791 3499 3391 2833
2707 3583 3307 2917 4733 1997 4133 2663
4397 2333 3797 2999 2371 3919 2971 3253
a(3) = 43680 corresponds to the following most-perfect magic square by S. Zorkin:
229 10457 859 9767 7393 3761 6763 4451
7841 3313 7211 4003 677 10009 1307 9319
953 9733 1583 9043 8117 3037 7487 3727
8623 2531 7993 3221 1459 9227 2089 8537
3527 7159 4157 6469 10691 463 10061 1153
10243 911 9613 1601 3079 7607 3709 6917
2803 7883 3433 7193 9967 1187 9337 1877
9461 1693 8831 2383 2297 8389 2927 7699
CROSSREFS
Sequence in context: A233882 A249625 A263036 * A295451 A084691 A084692
KEYWORD
nonn,more
AUTHOR
Natalia Makarova and Sergey Zorkin, Jul 04 2015
STATUS
approved

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Last modified May 20 08:05 EDT 2024. Contains 372703 sequences. (Running on oeis4.)