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

240, 29790, 24024

Offset: 2

Author

Natalia Makarova, May 23 2015

Keywords

• bref
• nonn
• more

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

• N. Makarova, Puzzle 671: Most Perfect Magic Squares, Prime Puzzles & Problems.
• Wikipedia, Most-perfect magic square

Crossrefs

Cf. A191533.