A079629 Number of twin prime pairs between p^2 and q^2 where (p,q) is the n-th twin prime pair.

2, 2, 2, 2, 2, 3, 5, 3, 7, 6, 6, 10, 13, 7, 8, 9, 9, 7, 12, 18, 14, 24, 19, 10, 21, 21, 20, 20, 19, 22, 19, 24, 24, 27, 25, 30, 27, 23, 34, 29, 21, 35, 38, 30, 32, 30, 33, 36, 33, 30

Offset: 1

Author

Paul Boddington, Jan 30 2003

Keywords

• easy
• nonn

Comments

Conjecturally a(n) is always positive. It seems that a(n) might tend to infinity.

Examples

			a(3)=2 because the third twin prime pair is (11,13) and there are 2 twin prime pairs between 121 and 169, namely (137,139) and (149,151).
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001359, A006512, A057767, A071538.

Cf. A137859, A137860.

Programs

Mathematica

ntpp[{a_,b_}]:=Count[Differences[Select[Range[a^2+1,b^2],PrimeQ]],2]; ntpp/@ Select[Partition[Prime[Range[300]],2,1],#[[2]]-#[[1]]==2&] (* Harvey P. Dale, Oct 04 2019 *)

Formula

a(n) = A071538(A006512(n)^2) - A071538(A001359(n)^2). - Reinhard Zumkeller, Feb 16 2008