A232393 Michael Stifel's 4 X 4 multiplication magic square read by rows.

32768, 4, 2, 4096, 256, 32, 64, 2048, 16, 512, 1024, 128, 8, 16384, 8192, 1

Offset

1,1

Comments

The square formed of natural numbers such that the products of the numbers of each row, each column and each diagonal are the same.

References

Jacques Sesiano, Les carrés magiques dans les pays islamiques, Lausanne: Presses polytechniques et universitaire romandes, 2004, p. 182.

Michael Stifel and Philipp Melanchton, Arithmetica integra, Nuremberg: Johannes Petreius, 1544, (29).

Links

Table of n, a(n) for n=1..16.

Eric Weisstein's World of Mathematics, Multiplication Magic Square

Wikipedia, Michael Stifel

Index entries for sequences related to magic squares

Example

The multiplication magic square is:
|-----|-----|-----|-----|
|32768|  4  |  2  | 4096|
|     |     |     |     |
|-----|-----|-----|-----|
| 256 |  32 |  64 | 2048|
|     |     |     |     |
|-----|-----|-----|-----|
|  16 | 512 | 1024| 128 |
|     |     |     |     |
|-----|-----|-----|-----|
|  8  |16384| 8192|  1  |
|     |     |     |     |
|-----|-----|-----|-----|
From Philippe Deléham, Nov 25 2013: (Start)
It is :
2^15, 2^2, 2^1, 2^12
2^8, 2^5, 2^6, 2^11
2^4, 2^9, 2^10, 2^7
2^3, 2^14, 2^13, 2^0, and the square:
|----|----|----|----|
| 15 | 2  | 1  | 12 |
|    |    |    |    |
|----|----|----|----|
| 8  | 5  | 6  | 11 |
|    |    |    |    |
|----|----|----|----|
| 4  | 9  | 10 |  7 |
|    |    |    |    |
|----|----|----|----|
| 3  | 14 | 13 |  0 |
|    |    |    |    |
|----|----|----|----|
is a magic square with constant = 30. (End)

Crossrefs

Sequence in context: A069416 A289478 A222528 * A217589 A069276 A195235

Adjacent sequences: A232390 A232391 A232392 * A232394 A232395 A232396

Keyword

nonn,fini,full,tabf

Author

Arkadiusz Wesolowski, Nov 23 2013

Status

approved