

A073502


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


4



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
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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 AndrewsSayles 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 TMM1.", 2008. (in Russian)
N. Makarova 13x13 magic square. (in Russian)
N. Makarova 14x14 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: A123727 A072807 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



