A170928 - OEIS

A170928

Least magic constant of magic squares using Smith numbers.

822, 1195, 1636, 2472, 3720, 5856, 8737, 12202, 16335, 21333, 27612, 35185, 43968, 54013, 65464, 78281, 92422, 107932, 126404, 147816, 171556, 197041, 224506, 253587, 285314, 320620, 359151, 400064, 442886, 487920, 536844, 589129, 644797

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OFFSET

3,1

COMMENTS

a(n) >= (1/n)*Sum_{i=1..n^2} A006753(i).

LINKS

Table of n, a(n) for n=3..35.

Natalia Makarova, Construction of smallest magic squares from Smith numbers (in Russian)

The square of order 4

The square of order 5

The square of order 6

The square of order 7

The square of order 9

EXAMPLE

Magic square of order 3: see the book: M. Gardner. From the Penrose tilings to securely encrypted, 1993:

94 382 346

526 274 22

202 166 454

The magic constant S = 822

Orders 4 to 6 are from participants of scientific forum dxdy.ru

The square of order 4:

22 346 562 265

778 274 85 58

4 454 382 355

391 121 166 517

S = 1195

The square of order 5:

355 576 4 319 382

454 85 391 648 58

27 535 346 526 202

706 166 378 121 265

94 274 517 22 729

S = 1636

The square of order 6:

729 4 636 762 22 319

27 663 654 526 85 517

391 645 58 378 438 562

382 346 454 121 634 535

355 648 94 483 627 265

588 166 576 202 666 274

CROSSREFS

Sequence in context: A002140 A095965 A059002 * A103764 A189121 A364538

Adjacent sequences: A170925 A170926 A170927 * A170929 A170930 A170931

KEYWORD

nonn,base

AUTHOR

Stefano Tognon, Feb 04 2010

EXTENSIONS

a(7), a(9) added by Natalia Makarova, Apr 02 2010

Edited by Max Alekseyev, May 26 2012

STATUS

approved