A243941 Number of decompositions of 36*n^2 into the sum of two twin prime pairs.

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, 30, 12, 14, 26, 16, 35, 16, 21, 22, 23, 38, 17, 28, 20, 36, 37, 16, 30, 27, 35, 33, 35, 29, 25, 34, 43, 51, 32, 44, 28, 39, 51, 40, 49, 31, 76, 31, 30, 52, 36, 103

Offset: 1

Author

Olivier Gérard, Jun 15 2014

Keywords

• nonn

Comments

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.

If there are only finitely many prime twins, this sequence will contain an infinite number of zeros.

Examples

			A solution is denoted by {p,q} where p,p+2,q,q+2 are all primes and p<=q.
a(10) = 8 because there are 8 ways to partition 3600 in this way.
The solution using the smallest prime numbers is 11+13+1787+1789 = 3600.
All 8 solutions are {11, 1787}, {101, 1697}, {179, 1619}, {191, 1607}, {311, 1487}, {347,1451}, {521, 1277} and {569, 1229}.
		

References

• Liang Ding Xiang, Problem 93#, Bulletin of Mathematics (Wuhan), 6 (1992), 41. ISSN 0488-7395.

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 terms from Andrew Howroyd)

Crossrefs

Cf. A016910 (36n^2).

Cf. A243940 (decompositions of n^2 into 4 primes).

Programs

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

Extensions

Liang reference from Alexander R. Povolotsky

Terms a(41) and beyond from Andrew Howroyd, Sep 17 2019