A240922 Magic constants of associative 4 X 4 X 4 cubes composed of distinct prime numbers.

1260, 1320, 1380, 1428, 1440, 1500, 1560, 1596, 1620

Offset

1,1

Comments

A magic cube is associative if the sum of its any two elements that are symmetric about the cube center equals the same number, called the associativity constant of the cube.

All magic 3 X 3 X 3 cubes are associative.

References

Andrews W. S. Magic Squares & Cubes, Dover Publ, 1960 (original publication Open Court, 1917)

William H. Benson and Oswald Jacoby. Magic Cubes. New Recreations. 1981.

Gakuho Abe, Related Magic Squares with Prime Elements, JRM 10:2 1977-78, pp.96-97.

A. W. Johnson, Jr., An Order 4 Prime Magic Cube, JRM 18:1, 1985-86, pp 5-7.

Links

Table of n, a(n) for n=1..9.

Harvey Heinz, Prime Number Magic Cubes

Natalia Makarova, Magic cubes corresponding to terms a(1)-a(6)

Discussion in forum dxdy.ru (in Russian)

Result for Magic Cubes of Prime Numbers

Example

a(1)=1260 corresponds to the following cube:
   23 521 433 283
  373  29 457 401
  587 139  11 523
  277 571 359  53
  ---------------
  263 379 557  61
  613  13 131 503
  317 449  31 463
   67 419 541 233
  ---------------
  397  89 211 563
  167 599 181 313
  127 499 617  17
  569  73 251 367
  ---------------
  577 271  59 353
  107 619 491  43
  229 173 601 257
  347 197 109 607

Crossrefs

Cf. A239671.

Sequence in context: A215991 A288921 A099592 * A014575 A144563 A175746

Adjacent sequences: A240919 A240920 A240921 * A240923 A240924 A240925

Keyword

nonn,more

Author

Natalia Makarova, Aug 02 2014

Status

approved