A088700 Number of primes between successive semiprimes.

1, 1, 0, 2, 0, 2, 0, 1, 0, 2, 0, 0, 1, 0, 2, 1, 0, 1, 0, 0, 2, 0, 1, 2, 0, 1, 1, 0, 0, 1, 0, 0, 0, 3, 2, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 2, 1, 0, 0, 1, 1, 1, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 3, 0, 2, 0, 1, 0, 1, 0, 1, 0, 2, 1, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0

Offset: 1

Author

Reinhard Zumkeller, Oct 08 2003

Keywords

• nonn

Comments

a(n) = 0 for almost all n. The average order of a(n) is 1/log log n. - Charles R Greathouse IV, Apr 29 2012

Examples

			a(34)=3, as there are three primes between A001358(34)=19*5=95 and A001358(34+1)=53*2=106: 97, 101 and 103.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Prime Counting Function
• Eric Weisstein's World of Mathematics, Semiprime

Crossrefs

Cf. A001358, (semiprimes), A088701, A103668 (semiprimes between primes).

Cf. A214520 (primes that are the only prime between consecutive semiprimes).

Programs

Mathematica

Select[Range[400], PrimeOmega[#] == 2&] // PrimePi // Differences (* Jean-François Alcover, Oct 12 2021 *)

Formula

a(n) = A000720(A001358(n+1)) - A000720(A001358(n));

a(A088701(n)) = n and a(k) <> n for 1 <= k < A088701(n).