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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
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 (list; graph; refs; listen; history; text; internal format)
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^2-1} 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^2-1} 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

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Last modified December 12 22:57 EST 2018. Contains 318081 sequences. (Running on oeis4.)