

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



2, 0, 1480028129, 31, 13, 7, 7, 79, 37, 23, 67, 89, 13, 89, 131, 31, 71, 47, 43, 73, 277, 353, 41, 67, 127, 223, 79, 13, 193, 5, 23, 43, 5, 67, 3, 19, 5, 59, 59, 653, 19, 19, 97, 409, 5, 383, 29, 137, 379, 349, 653, 1187, 47, 41, 37, 17, 619, 89, 283, 283, 43, 479, 191
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OFFSET

1,1


COMMENTS

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


REFERENCES

H. L. Nelson, Journal of Recreational Mathematics, 1988, vol. 20:3, p. 214.
Clifford A. Pickover, The Zen of Magic Squares, Circles and Stars: An Exhibition of Surprising Structures across Dimensions, Princeton University Press, 2002.


LINKS

Table of n, a(n) for n=1..63.
Harvey Heinz, Prime Magic Squares
Stefano Tognon, Table for prime magic squares
Index entries for sequences related to magic squares


FORMULA

Conjecture: for n > 4, a(n) = prime(s) where s > 1 is the smallest integer such that (Sum_{i=s..s+n^21} prime(i))/n is an integer of the same parity as n.  Max Alekseyev, Jan 29 2010
a(n) = prime(i) such that Sum_{k=0..n^21} prime(i+k) = n*A073520(n).  M. F. Hasler, Oct 29 2018


PROG

(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


CROSSREFS

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).
Sequence in context: A090446 A270830 A270829 * A073520 A152137 A097470
Adjacent sequences: A104154 A104155 A104156 * A104158 A104159 A104160


KEYWORD

hard,nonn


AUTHOR

Robert G. Wilson v, Mar 09 2005


EXTENSIONS

a(5)a(6) corrected, a(7)a(20) added by Max Alekseyev, Sep 24 2009
Definition edited by N. J. A. Sloane, Oct 03 2009
More terms from Max Alekseyev, Jan 29 2010


STATUS

approved



