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%I #30 Sep 18 2019 05:28:43
%S 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 30,12,14,26,16,35,16,21,22,23,38,17,28,20,36,37,16,30,27,35,33,35,29,
%U 25,34,43,51,32,44,28,39,51,40,49,31,76,31,30,52,36,103
%N Number of decompositions of 36*n^2 into the sum of two twin prime pairs.
%C 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 If there are only finitely many prime twins, this sequence will contain an infinite number of zeros.
%D Liang Ding Xiang, Problem 93#, Bulletin of Mathematics (Wuhan), 6 (1992), 41. ISSN 0488-7395.
%H 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 A solution is denoted by {p,q} where p,p+2,q,q+2 are all primes and p<=q.
%e a(10) = 8 because there are 8 ways to partition 3600 in this way.
%e The solution using the smallest prime numbers is 11+13+1787+1789 = 3600.
%e All 8 solutions are {11, 1787}, {101, 1697}, {179, 1619}, {191, 1607}, {311, 1487}, {347,1451}, {521, 1277} and {569, 1229}.
%o (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 Cf. A016910 (36n^2).
%Y Cf. A243940 (decompositions of n^2 into 4 primes).
%K nonn
%O 1,2
%A _Olivier Gérard_, Jun 15 2014
%E Liang reference from _Alexander R. Povolotsky_
%E Terms a(41) and beyond from _Andrew Howroyd_, Sep 17 2019
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