A192227 Number of primes in the range (n - 2*sqrt(sqrt(n)), n].

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

Offset: 1

Author

Juri-Stepan Gerasimov, Jun 26 2011

Keywords

• nonn

Comments

a(n) is probably positive for all n > 191913030. - Charles R Greathouse IV, Jul 01 2011

Crossrefs

Cf. A188817, A189025, A192226.

Programs

Maple

A192227 := proc(n) local nhi, nlo ; nhi := n ; nlo := floor( n-2*root[4](n)) ; numtheory[pi](nhi)-numtheory[pi](nlo) ; end proc; # R. J. Mathar, Jul 12 2011

Mathematica

Table[PrimePi[n]-PrimePi[n-2*Sqrt[Sqrt[n]]],{n,90}] (* Harvey P. Dale, Feb 24 2018 *)

Formula

Conjecturally, a(n) ~ 2*n^(1/4)/log n. - Charles R Greathouse IV, Jul 01 2011