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A240922 Magic constants of associative 4 X 4 X 4 cubes composed of distinct prime numbers. 1
1260, 1320, 1380, 1428, 1440, 1500, 1560, 1596, 1620 (list; graph; refs; listen; history; text; internal format)
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.

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

Harvey Heinz, Prime Number Magic Cubes

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

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Last modified February 19 07:39 EST 2018. Contains 299330 sequences. (Running on oeis4.)