This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
The square is [ 43 1 67 / 61 37 13 / 7 73 31 ].
The square is [101 5 71 ; 29 59 89 ; 47 113 17]. The lexicographically smallest equivalent variant (modulo reflections on the symmetry axes of the square) is [17 89 71 ; 113 59 5 ; 47 29 101], cf. A320872. - _M. F. Hasler_, Oct 24 2018
A024351=select(p->setsearch(P,118-p),P=primes(30)[^5]) \\ 118 = 2*59, where 59 is the central prime; primes(30) = primes < 118. For the magic square itself, use A320872_row(1). - M. F. Hasler, Oct 25 2018
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.
From _A.H.M. Smeets_, Mar 10 2021: (Start)
The case a(1) = 1 is trivial.
In case a(2) = 2, the set of potential magic square numbers is {1, 3, 5, 7} with potential magic constant 8, however, no magic square exists of order 2.
In case a(4) = 12, not only the potential magic constant exists, but also the magic square itself, as shown by Stefano Tognon or Eric Weisstein's World of Mathematics. (End)
The magic square is: [ 1 823 821 809 811 797 19 29 313 31 23 37 ] [ 89 83 211 79 641 631 619 709 617 53 43 739 ] [ 97 227 103 107 193 557 719 727 607 139 757 281 ] [ 223 653 499 197 109 113 563 479 173 761 587 157 ] [ 367 379 521 383 241 467 257 263 269 167 601 599 ] [ 349 359 353 647 389 331 317 311 409 307 293 449 ] [ 503 523 233 337 547 397 421 17 401 271 431 433 ] [ 229 491 373 487 461 251 443 463 137 439 457 283 ] [ 509 199 73 541 347 191 181 569 577 571 163 593 ] [ 661 101 643 239 691 701 127 131 179 613 277 151 ] [ 659 673 677 683 71 67 61 47 59 743 733 41 ] [ 827 3 7 5 13 11 787 769 773 419 149 751 ]
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