A073502 The smallest magic constant for n X n magic square with prime entries (regarding 1 as a prime).

111, 102, 213, 408, 699, 1114, 1681, 2416, 3355, 4514, 5937, 7626, 9635, 11986, 14691, 17818, 21373, 25394, 29873, 34926, 40511, 46664, 53445, 60898, 69045, 77888, 87473, 97850, 109065, 121126, 134113, 147982, 162759

Offset

3,1

Comments

Until the early part of the twentieth century 1 was regarded as a prime (see A008578).

References

W. S. Andrews and H. A. Sayles, The Monist (Chicago) for October 1913.

H. E. Dudeney, Amusements in Mathematics, Nelson, London, 1917, page 125, who quotes the Andrews-Sayles article as his source.

Links

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

Yu. V. Chebrakov, Section 3.3. Smallest magic matrices of prime numbers in "Theory of Magic Matrices. Issue TMM-1.", 2008. (in Russian)

N. Makarova 13 X 13 magic square. (in Russian)

N. Makarova 14 X 14 magic square. (in Russian)

Eric Weisstein's World of Mathematics, Prime Magic Square

Index entries for sequences related to magic squares

Crossrefs

Cf. A073473 (for the n=3 square), A024351, A073520, A164843, A173079.

Sequence in context: A282976 A284083 A252724 * A066335 A107844 A084504

Adjacent sequences: A073499 A073500 A073501 * A073503 A073504 A073505

Keyword

nonn,more

Author

N. J. A. Sloane, Aug 27 2002

Extensions

Dudeney gives 36095/11 for n = 11 (an obvious typo) and 4514 for n = 12

a(3)-a(12) are confirmed/given by Chebrakov

a(15), a(17), a(22), a(35), and a(124)=9912840 from S. Tognon (cf. A173079)

a(13)-a(14), a(16), a(18)-a(21), a(23)-a(34) from N. Makarova

Edited by Max Alekseyev, Feb 11 2010

Status

approved