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

1,4

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

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

Formula

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

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

Example

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.

Mathematica

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

Crossrefs

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

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

Sequence in context: A039973 A035171 A352567 * A287121 A035446 A126211

Adjacent sequences: A088697 A088698 A088699 * A088701 A088702 A088703

Keyword

nonn

Author

Reinhard Zumkeller, Oct 08 2003

Status

approved