report on sequences from magic squares of primes

N. J. A. Sloane njas at research.att.com
Thu Aug 29 16:16:09 CEST 2002


Thanks to Divid Wilson for pointing out Harvey Heinz's very nice web page.

The OEIS now contains the following:

%I A073520
%S A073520 2,0,4440084513,258,1703,930
%N A073520 Smallest magic constant for any n X n magic square made from consecutive primes, or 0 if no such magic square exists.
%D A073520 H. L. Nelson, Journal of Recreational Mathematics, 1988, vol. 20:3, p. 214.
%H A073520 Harvey Heinz, <a href="http://www.geocities.com/CapeCanaveral/Launchpad/4057/primesqr.htm">Prime Magic Squares</a>
%H A073520 <a href="http://www.research.att.com/~njas/sequences/Sindx_Mag.html#magic">Index entries for sequences related to magic squares</a>
%O A073520 1,1
%Y A073520 For the magic squares of orders 3 through 6 see A073519, A073521, A073522, A073523.
%K A073520 nonn,nice,more,hard
%A A073520 njas, Aug 29 2002

If the primes don't need to be consecutive then all I know is that
the sequence begins 2,0,177.  Can anyone supply more terms?

If 1 is counted as a prime, and the primes don't need to be consecutive, then we have:

%I A073502
%S A073502 111,102,213,408,699,1114,1681,2416
%N A073502 Magic constant for n X n magic square with prime entries (regarding 1 as a prime) with smallest row sums.
%C A073502 Until the early part of the twentieth century 1 was regarded as a prime (cf. A008578).
%C A073502 I don't know how far these entries have been rigorously computed. Lee Sallows has confirmed the first term (cf. A073473).
%D A073502 W. S. Andrews and H. A. Sayles, The Monist (Chicago) for October 1913.
%D A073502 H. E. Dudeney, Amusements in Mathematics, Nelson, London, 1917, page 125, who quotes the Andrews-Sayles article as his source.
%H A073502 <a href="http://www.research.att.com/~njas/sequences/Sindx_Mag.html#magic">Index entries for sequences related to magic squares</a>
%Y A073502 Cf. A073473 (for the n=3 square), A024351.
%K A073502 nonn,new
%O A073502 3,1
%A A073502 njas, Aug 27 2002
%E A073502 What is the analogous sequence when 1 is not allowed? All I know is that it begins with 177 (see A024351).
%E A073502 Dudeney gives 36095/11 for n = 11 (an obvious typo) and 4514 for n = 12.

Only the first term has been confirmed - can anyone help
with subsequent terms?

Neil Sloane, njas at research.att.com








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