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A164843 The smallest magic constant of an n X n magic square with distinct prime entries. 6
177, 120, 233, 432, 733, 1154, 1731, 2470, 3417, 4584, 6013, 7712, 9731, 12088, 14807, 17940, 21501, 25530, 30021, 35086, 40675, 46840, 53631, 61092, 69251, 78100, 87697, 98084, 109309, 121380, 134377, 148258, 163043 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

COMMENTS

a(n) >= m(n), where m(n) is the smallest integer of the same parity as n, which is >= (sum_{k=1..n^2} prime(k+1))/n. For example, sum_{k=1..5^2} prime(k+1)/5=231.8, so m(5)=233. Conjecture: for n>4, a(n)=m(n) or a(n)=m(n)+2.

LINKS

Table of n, a(n) for n=3..35.

Harvey Heinz, Prime magic squares

A. Lelechenko and N. Makarova, Examples of prime magic n X n squares with minimal magic constant for n=5..13.

N. Makarova, Smallest prime magic squares, Part I (in Russian)

N. Makarova, Smallest prime magic squares, Part II (in Russian)

Mathworld, Prime magic squares

PlanetMath, Prime magic squares

Stefano Tognon, Prime Analysis

EXAMPLE

From Natalia Makarova, Sep 26 2009 (Start)

Here is a 14 X 14 example:

[3 43 59 131 181 271 383 599 797 919 971 1039 1123 1193

1151 433 967 211 337 491 397 691 83 523 593 773 449 613

263 373 101 1063 877 617 419 911 787 241 151 839 739 331

503 439 809 1051 1091 659 157 1031 71 139 379 179 743 461

173 647 1069 389 1049 19 311 223 317 1103 283 947 499 683

547 13 1061 353 229 853 677 751 571 983 1201 29 193 251

643 269 887 733 23 409 1129 191 769 401 47 1109 149 953

163 881 673 107 431 487 991 631 829 109 349 367 811 883

1163 827 607 1171 443 653 463 5 457 577 31 293 601 421

509 1097 313 757 167 709 761 347 857 137 619 233 89 1117

1093 1019 7 521 1033 61 73 941 1009 859 701 11 127 257

53 467 97 307 1153 557 1021 569 359 937 821 113 977 281

907 17 823 641 661 929 67 719 79 587 479 563 1013 227

541 1187 239 277 37 997 863 103 727 197 1087 1217 199 41] (End)

Comment from N. J. A. Sloane, Sep 28 2009: this contains 192 consecutive primes, 3 to 1171, plus 1187, 1193, 1201, 1217.

For the 3 X 3 case see A024351. For the 4 X 4 magic square see the Mathworld link.

CROSSREFS

Cf. A073502, A073350, A125007.

Sequence in context: A159442 A046189 A278198 * A268790 A077786 A188537

Adjacent sequences:  A164840 A164841 A164842 * A164844 A164845 A164846

KEYWORD

nonn,more

AUTHOR

Andrew Lelechenko, Aug 28 2009 and Natalia Makarova, Sep 08 2009

EXTENSIONS

Partially reworded by R. J. Mathar, Aug 31 2009

Edited by N. J. A. Sloane, Sep 14 2009

a(11)-a(15) from N. Makarova, a(16)-a(35) from N. Makarova and S. Tognon.

Edited by Max Alekseyev, Feb 11 2010

STATUS

approved

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Last modified November 23 00:33 EST 2017. Contains 295107 sequences.