A176811 Number of primes between 2*(lesser of n-th twin prime pair) and 2*(greater of n-th twin prime pair).

1, 2, 1, 1, 2, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 2, 2, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 2, 1, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 2, 1, 0, 2, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1

Offset: 1

Author

Juri-Stepan Gerasimov, Apr 26 2010

Keywords

• nonn

Comments

Number of primes between 2*A001359(n) and 2*A006512(n).

Number of primes between A108605(n) and A176810(n).

Number of primes between 2*A077800(2n-1) and 2*A077800(2n).

Examples

			a(1)=1 because 2*3 < 7 (prime) < 2*5;
a(2)=2 because 2*5 < 11 (prime) < 13(prime) < 2*7;
a(3)=1 because 2*11 < 23 (prime) < 2*13.
		

Crossrefs

Cf. A001359, A006512, A077800, A108605, A176810.

Programs

Maple

A001359 := proc(n) option remember; if n = 1 then 3; else for a from procname(n-1)+2 by 2 do if isprime(a) and isprime(a+2) then return a; end if; end do: end if; end proc:
A006512 := proc(n) A001359(n)+2 ; end proc:
A176811 := proc(n) numtheory[pi](2*A006512(n)) - numtheory[pi](2*A001359(n)) ; end proc:
seq(A176811(n),n=1..120) ; # R. J. Mathar, Apr 27 2010

Mathematica

PrimePi[2*#[[2]]]-PrimePi[2*#[[1]]]&/@Select[Partition[Prime[Range[1000]],2,1],#[[2]]- #[[1]] == 2&] (* Harvey P. Dale, Jul 21 2023 *)

Extensions

Terms corrected starting at a(34) by R. J. Mathar, Apr 27 2010