A192393 Number of primes in the half-open interval [semiprime(n)-sqrt(semiprime(n)), semiprime(n)).

2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 3, 4, 3, 2, 2, 1, 1, 1, 1, 2, 2, 3, 3, 2, 2, 2, 2, 3, 3, 3, 2, 3, 2, 2, 3, 3, 2, 3, 4, 4, 4, 4, 3, 2, 2, 1, 1, 1, 1, 1, 1, 2, 4, 4, 3, 2, 3, 3, 2, 2, 3, 3

Offset

1,1

Links

Table of n, a(n) for n=1..86.

Formula

Conjecturally, a(n) ~ sqrt(n log log n / (log n)^3). - Charles R Greathouse IV, Jun 29 2011

Example

a(1)=2 because 2 and 3 are in range [semiprime(1)-sqrt(semiprime(1)), semiprime(1))=[2, 4).

Maple

A192393 := proc(n) local phi, plo;  phi := A001358(n)-1 ; plo := ceil(A001358(n) -sqrt(A001358(n)))-1 ; numtheory[pi](phi)-numtheory[pi](plo) ; end proc: # R. J. Mathar, Jul 12 2011

Crossrefs

Cf. A001358.

Sequence in context: A242481 A228287 A213636 * A184303 A218545 A205600

Adjacent sequences: A192390 A192391 A192392 * A192394 A192395 A192396

Keyword

nonn,less

Author

Juri-Stepan Gerasimov, Jun 29 2011

Extensions

Corrected by R. J. Mathar, Jul 12 2011

Status

approved