

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.


0



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


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 evenness as n.  Max Alekseyev, Jan 29 2010


CROSSREFS

Cf. A073519, A073520, A073521, A073522, A073523.
Sequence in context: A114632 A036108 A090446 * A073520 A152137 A060838
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



