A079629 - OEIS

%I #16 Mar 21 2023 06:10:21

%S 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,

%T 19,22,19,24,24,27,25,30,27,23,34,29,21,35,38,30,32,30,33,36,33,30

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

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

%H Harvey P. Dale, <a href="/A079629/b079629.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = A071538(A006512(n)^2) - A071538(A001359(n)^2). - _Reinhard Zumkeller_, Feb 16 2008

%e 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).

%t 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 *)

%Y Cf. A001359, A006512, A057767, A071538.

%Y Cf. A137859, A137860.

%K easy,nonn

%O 1,1

%A _Paul Boddington_, Jan 30 2003