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A104157 Smallest of n^2 consecutive primes that form an n X n magic square with the least magic constant, or 0 if no such magic square exists. 6


%S 2,0,1480028129,31,13,7,7,79,37,23,67,89,13,89,131,31,71,47,43,73,277,

%T 353,41,67,127,223,79,13,193,5,23,43,5,67,3,19,5,59,59,653,19,19,97,

%U 409,5,383,29,137,379,349,653,1187,47,41,37,17,619,89,283,283,43,479,191

%N Smallest of n^2 consecutive primes that form an n X n magic square with the least magic constant, or 0 if no such magic square exists.

%C The magic constants (= sums) are given in A073520. For a given sum, the corresponding list of primes (and thus also the smallest one) is easily calculated, cf. PARI code. - _M. F. Hasler_, Oct 29 2018

%D H. L. Nelson, Journal of Recreational Mathematics, 1988, vol. 20:3, p. 214.

%D Clifford A. Pickover, The Zen of Magic Squares, Circles and Stars: An Exhibition of Surprising Structures across Dimensions, Princeton University Press, 2002.

%H Harvey Heinz, <a href="http://www.magic-squares.net/primesqr.htm">Prime Magic Squares</a>

%H Stefano Tognon, <a href="http://digilander.libero.it/ice00/magic/prime/orderConstant.html">Table for prime magic squares</a>

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

%F Conjecture: for n > 4, a(n) = prime(s) where s > 1 is the smallest integer such that (Sum_{i=s..s+n^2-1} prime(i))/n is an integer of the same parity as n. - _Max Alekseyev_, Jan 29 2010

%F a(n) = prime(i) such that Sum_{k=0..n^2-1} prime(i+k) = n*A073520(n). - _M. F. Hasler_, Oct 29 2018

%o (PARI) A104157(n)=MagicPrimes(A073520[n],n)[1] \\ See A073519 for MagicPrimes(). This code uses a precomputed array A073520, but in practice one would rather compute that sequence as function of this one. - _M. F. Hasler_, Oct 29 2018

%Y Cf. A073519 or A320873 (the square for 3 X 3), A073520 (magic sums for 4 X 4 squares of consecutive primes), A073521 (consecutive primes of a 4 X 4 magic square), A073522 (consecutive primes of a (non minimal!) 5 X 5 magic square), A073523 (consecutive primes of a pandiagonal 6 X 6 magic square).

%K hard,nonn

%O 1,1

%A _Robert G. Wilson v_, Mar 09 2005

%E a(5)-a(6) corrected, a(7)-a(20) added by _Max Alekseyev_, Sep 24 2009

%E Definition edited by _N. J. A. Sloane_, Oct 03 2009

%E More terms from _Max Alekseyev_, Jan 29 2010

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Last modified March 25 16:33 EDT 2019. Contains 321474 sequences. (Running on oeis4.)