A103668 Number of semiprimes between prime(n) and prime(n+1).

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, 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, 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

Offset: 1

Author

Zak Seidov, Feb 12 2005

Keywords

• base
• nonn

Examples

			a(4)=2 because between prime(4)=7 and prime(5)=11 there are two semiprimes: 3*3 and 2*5.
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.
		

Links

• T. D. Noe, Table of n, a(n) for n=1..1000

Crossrefs

The first occurrence of k = 0, 1, 2, ... is at position 1, 2, 4, 11, 24, 34, 30, 47, ... (A103669).

Primes: A000040, semiprimes: A001358, number of primes between two successive semiprimes: A088700.

Cf. A103654, A103655, A103669.

Programs

Mathematica

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 *)
Table[Count[Range[Prime[n],Prime[n+1]],?(PrimeOmega[#]==2&)],{n,110}] (* _Harvey P. Dale, Sep 29 2019 *)