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.
%I A191533 #40 Feb 04 2024 21:26:02
%S A191533 240,252,288,372,408,420,480,492,504,528,540,552,560,564,576,588,600,
%T A191533 612,620,624,648,660,672,680,684,708,720,728,732,740,756,768,780,792,
%U A191533 800,816,828,836,840,848,852,860,864,876,888,900,912,920,924,936,948
%N A191533 Magic constants of pandiagonal magic squares of order 4 composed of distinct primes.
%C A191533 A pandiagonal square of order 4 consists of 8 pairs of complementary numbers with the sum in each pair equal to S/2 (where S is the magic constant). For example, the array {7, 113, 11, 109, 13, 107, 17, 103, 19, 101, 23, 97, 31, 89, 37, 83, 41, 79, 47, 73, 53, 67, 59, 61} consists of 12 complementary prime pairs with the sum 7 + 113 = 11 + 109 = ... = 59 + 61 = 120 = S/2.
%C A191533 Pandiagonal squares of order 4 are also the most-perfect squares.
%C A191533 There is a one-to-one correspondence between pandiagonal and associative magic squares of order 4. Any pandiagonal square can be turned into an associative square by rearrangements of its rows and columns, and vice versa.
%C A191533 For example, pandiagonal square:
%C A191533 [ 13 83 31 113
%C A191533 97 47 79 17
%C A191533 89 7 107 37
%C A191533 41 103 23 73 ]
%C A191533 the corresponding associative square:
%C A191533 [ 13 83 113 31
%C A191533 97 47 17 79
%C A191533 41 103 73 23
%C A191533 89 7 37 107]
%C A191533 Magic constants of pandiagonal magic squares of order 4 are always multiples of 4. It looks as though most sufficiently large multiples of 4 are magic constants of some pandiagonal magic squares of order 4. For multiples of 4 between 3000 and 10000, only 3028, 3208, 3436, 3664, 4436, 4504, and 5116 are not the magic constant of any pandiagonal magic squares of order 4. - _Zhao Hui Du_, Jan 09 2024
%H A191533 Max Alekseyev, <a href="/A191533/b191533.txt">Table of n, a(n) for n = 1..100</a>
%H A191533 Natalia Makarova, <a href="http://www.natalimak1.narod.ru/pand4.htm">Order-4 pandiagonal magic squares composed of primes</a> (in Russian)
%e A191533 a(3)=288 for the matrix
%e A191533 [ 7 127 41 113
%e A191533 71 83 37 97
%e A191533 103 31 137 17
%e A191533 107 47 73 61 ]
%Y A191533 Cf. A179440.
%K A191533 nonn
%O A191533 1,1
%A A191533 _Natalia Makarova_, Jun 05 2011
%E A191533 Terms a(18) onward from _Max Alekseyev_, May 26 2012