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 A243941 #30 Sep 18 2019 05:28:43
%S A243941 1,2,2,5,5,3,6,3,6,8,5,6,7,6,10,10,9,8,15,10,13,8,23,5,16,21,10,20,13,
%T A243941 30,12,14,26,16,35,16,21,22,23,38,17,28,20,36,37,16,30,27,35,33,35,29,
%U A243941 25,34,43,51,32,44,28,39,51,40,49,31,76,31,30,52,36,103
%N A243941 Number of decompositions of 36*n^2 into the sum of two twin prime pairs.
%C A243941 Following a remark of M. T. Kong Tong on seqfan, there seems to be always at least one way to partition (6n)^2 into the sum of two prime pairs. This sequence gives the number of different solutions.
%C A243941 If there are only finitely many prime twins, this sequence will contain an infinite number of zeros.
%D A243941 Liang Ding Xiang, Problem 93#, Bulletin of Mathematics (Wuhan), 6 (1992), 41. ISSN 0488-7395.
%H A243941 David A. Corneth, <a href="/A243941/b243941.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Andrew Howroyd)
%e A243941 A solution is denoted by {p,q} where p,p+2,q,q+2 are all primes and p<=q.
%e A243941 a(10) = 8 because there are 8 ways to partition 3600 in this way.
%e A243941 The solution using the smallest prime numbers is 11+13+1787+1789 = 3600.
%e A243941 All 8 solutions are {11, 1787}, {101, 1697}, {179, 1619}, {191, 1607}, {311, 1487}, {347,1451}, {521, 1277} and {569, 1229}.
%o A243941 (PARI) a(n)={my(m=18*n^2, s=0); forprime(p=5, m/2, if(isprime(m-p) && isprime(p-2) && isprime(m-p+2), s++)); s} \\ _Andrew Howroyd_, Sep 17 2019
%Y A243941 Cf. A016910 (36n^2).
%Y A243941 Cf. A243940 (decompositions of n^2 into 4 primes).
%K A243941 nonn
%O A243941 1,2
%A A243941 _Olivier Gérard_, Jun 15 2014
%E A243941 Liang reference from _Alexander R. Povolotsky_
%E A243941 Terms a(41) and beyond from _Andrew Howroyd_, Sep 17 2019