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

1,1

Comments

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

Links

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

Formula

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

Example

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).

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 *)

Crossrefs

Cf. A001359, A006512, A057767, A071538.

Cf. A137859, A137860.

Sequence in context: A029105 A079954 A114968 * A029116 A064770 A322073

Adjacent sequences: A079626 A079627 A079628 * A079630 A079631 A079632

Keyword

easy,nonn

Author

Paul Boddington, Jan 30 2003

Status

approved