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

1,2

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).

Links

Table of n, a(n) for n=1..105.

Example

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.

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 *)

Crossrefs

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

Sequence in context: A117586 A307988 A268917 * A057594 A259029 A286128

Adjacent sequences: A176808 A176809 A176810 * A176812 A176813 A176814

Keyword

nonn

Author

Juri-Stepan Gerasimov, Apr 26 2010

Extensions

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

Status

approved