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A073502 The smallest magic constant for n X n magic square with prime entries (regarding 1 as a prime). 5

%I #16 Oct 27 2019 21:42:35

%S 111,102,213,408,699,1114,1681,2416,3355,4514,5937,7626,9635,11986,

%T 14691,17818,21373,25394,29873,34926,40511,46664,53445,60898,69045,

%U 77888,87473,97850,109065,121126,134113,147982,162759

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

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

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

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

%H Yu. V. Chebrakov, <a href="http://chebrakov.narod.ru/bbb-3.3.pdf">Section 3.3. Smallest magic matrices of prime numbers</a> in "Theory of Magic Matrices. Issue TMM-1.", 2008. (in Russian)

%H N. Makarova <a href="http://dxdy.ru/post242834.html#p242834">13 X 13 magic square</a>. (in Russian)

%H N. Makarova <a href="http://dxdy.ru/post245184.html#p245184">14 X 14 magic square</a>. (in Russian)

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeMagicSquare.html">Prime Magic Square</a>

%H <a href="/index/Mag#magic">Index entries for sequences related to magic squares</a>

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

%K nonn,more

%O 3,1

%A _N. J. A. Sloane_, Aug 27 2002

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

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

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

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

%E Edited by _Max Alekseyev_, Feb 11 2010

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