%I #11 Sep 29 2019 14:08:53
%S 0,1,1,2,0,2,0,2,2,0,3,2,0,1,2,3,0,2,1,0,2,1,3,4,0,0,1,0,1,6,1,2,0,5,
%T 0,1,3,1,1,2,0,3,0,1,0,6,7,1,0,0,2,0,2,2,2,2,0,1,1,0,3,7,1,0,1,6,2,3,
%U 0,0,2,3,1,1,2,1,4,1,2,4,0,2,0,1,0,3,3,1,0,1,4,3,1,2,2,1,5,0,7,3,3,2,2,0,1
%N Number of semiprimes between prime(n) and prime(n+1).
%H T. D. Noe, <a href="/A103668/b103668.txt">Table of n, a(n) for n=1..1000</a>
%e a(4)=2 because between prime(4)=7 and prime(5)=11 there are two semiprimes: 3*3 and 2*5.
%e a(11)=3 because between p(11)=31 and p(12)=37 there are three semiprimes: 33=3*11, 34=2*17 and 35=5*7.
%t fQ[n_] := Plus @@ Last /@ FactorInteger[n] == 2; f[n_] := Count[fQ /@ Range[Prime[n] + 1, Prime[n + 1] - 1], True]; Table[ f[n], {n, 105}] (* _Robert G. Wilson v_, May 07 2005 *)
%t Table[Count[Range[Prime[n],Prime[n+1]],_?(PrimeOmega[#]==2&)],{n,110}] (* _Harvey P. Dale_, Sep 29 2019 *)
%Y The first occurrence of k = 0, 1, 2, ... is at position 1, 2, 4, 11, 24, 34, 30, 47, ... (A103669).
%Y Primes: A000040, semiprimes: A001358, number of primes between two successive semiprimes: A088700.
%Y Cf. A103654, A103655, A103669.
%K base,nonn
%O 1,4
%A _Zak Seidov_, Feb 12 2005