cp's OEIS Frontend

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

%I A176811 #11 Jul 21 2023 14:06:13
%S A176811 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,
%T A176811 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,
%U A176811 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
%N A176811 Number of primes between 2*(lesser of n-th twin prime pair) and 2*(greater of n-th twin prime pair).
%C A176811 Number of primes between 2*A001359(n) and 2*A006512(n).
%C A176811 Number of primes between A108605(n) and A176810(n).
%C A176811 Number of primes between 2*A077800(2n-1) and 2*A077800(2n).
%e A176811 a(1)=1 because 2*3 < 7 (prime) < 2*5;
%e A176811 a(2)=2 because 2*5 < 11 (prime) < 13(prime) < 2*7;
%e A176811 a(3)=1 because 2*11 < 23 (prime) < 2*13.
%p A176811 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:
%p A176811 A006512 := proc(n) A001359(n)+2 ; end proc:
%p A176811 A176811 := proc(n) numtheory[pi](2*A006512(n)) - numtheory[pi](2*A001359(n)) ; end proc:
%p A176811 seq(A176811(n),n=1..120) ; # _R. J. Mathar_, Apr 27 2010
%t A176811 PrimePi[2*#[[2]]]-PrimePi[2*#[[1]]]&/@Select[Partition[Prime[Range[1000]],2,1],#[[2]]- #[[1]] == 2&] (* _Harvey P. Dale_, Jul 21 2023 *)
%Y A176811 Cf. A001359, A006512, A077800, A108605, A176810.
%K A176811 nonn
%O A176811 1,2
%A A176811 _Juri-Stepan Gerasimov_, Apr 26 2010
%E A176811 Terms corrected starting at a(34) by _R. J. Mathar_, Apr 27 2010