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 A073523 The set of 36 consecutive primes that form a 6 X 6 pandiagonal magic square with the smallest magic constant (930). 11
 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS There exist non-pandiagonal 6 X 6 magic squares composed of consecutive primes with smaller magic constant, the smallest being A073520(6) = 484. Pandiagonal means that not only the 2 main diagonals, but all other 10 diagonals also have the same sum, Sum_{i=1..6} A[i,M6(k +/- i)] = 930 for k = 1, ..., 6 and M6(x) = y in {1, ..., 6} such that y == x (mod 6). - M. F. Hasler, Oct 20 2018 See A320876 for the primes in the order in which they appear in the matrix. - M. F. Hasler, Oct 22 2018 REFERENCES Allan W. Johnson, Jr., Journal of Recreational Mathematics, vol. 23:3, 1991, pp. 190-191. 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..36. Harvey Heinz, Prime Magic Squares Index entries for sequences related to magic squares EXAMPLE The magic square is [ 67 193 71 251 109 239 ] [ 139 233 113 181 157 107 ] [ 241 97 191 89 163 149 ] [ 73 167 131 229 151 179 ] [ 199 103 227 101 127 173 ] [ 211 137 197 79 223 83 ] PROG (PARI) A073523=MagicPrimes(930, 6) \\ See A073519 for MagicPrimes(). - M. F. Hasler, Oct 22 2018 CROSSREFS Cf. A073519 and A320873 (3 X 3 magic square of consecutive primes), A073521 (consecutive primes of a 4 X 4 magic square), A245721 and A320874 (consecutive primes of a 4 X 4 pandigital magic square), A073522 (consecutive primes of a 5 X 5 magic square, not minimal and not pan-diagonal). Cf. A256234: magic sums of 4 X 4 pandiagonal magic squares of consecutive primes, A073520: magic sums for n X n squares of consecutive primes. Sequence in context: A246783 A169936 A045808 * A295803 A033243 A241897 Adjacent sequences: A073520 A073521 A073522 * A073524 A073525 A073526 KEYWORD nonn,fini,full AUTHOR N. J. A. Sloane, Aug 29 2002 EXTENSIONS Edited by Max Alekseyev, Sep 24 2009 Edited by M. F. Hasler, Oct 29 2018 STATUS approved

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Last modified May 28 14:39 EDT 2023. Contains 363019 sequences. (Running on oeis4.)