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

1,2

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.

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)

Example

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}.

Prog

(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

Crossrefs

Cf. A016910 (36n^2).

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

Sequence in context: A357123 A253600 A045537 * A161622 A116559 A210802

Adjacent sequences: A243938 A243939 A243940 * A243942 A243943 A243944

Keyword

nonn

Author

Olivier Gérard, Jun 15 2014

Extensions

Liang reference from Alexander R. Povolotsky

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

Status

approved