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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A258082 Smallest magic constant of most-perfect magic squares of order 2n composed of distinct prime numbers.

Original entry on oeis.org

240, 29790, 24024
Offset: 2

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Author

Natalia Makarova, May 23 2015

Keywords

Comments

A magic square of order 2n is most-perfect if the following two conditions hold: (i) every 2 x 2 subsquare (including wrap-around) sum to 2T; and (ii) any pair of elements at distance n along a diagonal or a skew diagonal sum to T, where T= S/n, S is the magic constant.
All most-perfect magic squares are pandiagonal.
All pandiagonal magic squares of order 4 are most-perfect (cf. A191533).

Examples

			a(3)=29790 corresponds to the following most-perfect magic square of order 6:
   149 9161 2309 6701 2609 8861
  9067 1483 6907 3943 6607 1783
  4139 5171 6299 2711 6599 4871
  3229 7321 1069 9781  769 7621
  5987 3323 8147  863 8447 3023
  7219 3331 5059 5791 4759 3631
a(4)=24024 corresponds to the following most-perfect magic square of order 8:
    19 5923 1019 4423 4793 1277 3793 2777
  4877 1193 3877 2693  103 5839 1103 4339
   499 5443 1499 3943 5273  797 4273 2297
  5297  773 4297 2273  523 5419 1523 3919
  1213 4729 2213 3229 5987   83 4987 1583
  5903  167 4903 1667 1129 4813 2129 3313
   733 5209 1733 3709 5507  563 4507 2063
  5483  587 4483 2087  709 5233 1709 3733

Links

Crossrefs

Cf. A191533.

A258755 The magic constants of most-perfect magic squares of order 6 composed of distinct prime numbers.

Original entry on oeis.org

29790, 37530, 46002, 46050, 47502, 52290, 61110
Offset: 1

Views

Author

Natalia Makarova, Jun 09 2015

Keywords

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.
The magic constants of most-perfect magic squares of order 4 composed of distinct primes see A191533.
The minimal magic constant of most-perfect magic square of order 6 composed of distinct primes corresponds to a(1) = 29790, see A258082.
The seven terms shown have been verified by exhaustive search. - Natalia Makarova, Jun 09 2016

Examples

			a(2) = 37530 corresponds to the following most-perfect magic square:
   4919  9181  4049  6151  7949  5281
   9293  1627 10163  4657  6263  5527
   3833 10267  2963  7237  6863  6367
   6359  4561  7229  7591  3329  8461
   7853  6247  6983  3217 10883  2347
   5273  5647  6143  8677  2243  9547
a(3) = 46002 corresponds to the following most-perfect magic square:
   6053 14321  2417  6473 13901  2837
  10061   233 13697  8081  2213 11717
   5483 14891  1847  7043 13331  3407
   8861  1433 12497  9281  1013 12917
   7253 13121  3617  5273 15101  1637
   8291  2003 11927  9851   443 13487

Links

Crossrefs

Cf. A191533, A258082.

A259733 The magic constants of most-perfect magic squares of order 8 composed of distinct prime numbers.

Original entry on oeis.org

24024, 26040, 43680, 44352, 44520, 44880
Offset: 1

Views

Author

Natalia Makarova and Sergey Zorkin, Jul 04 2015

Keywords

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

Examples

			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

Links

Crossrefs

Cf. A191533, A258082, A258755.
Showing 1-3 of 3 results.

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