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Number of primes in the range (n - 2*sqrt(sqrt(n)), n].
1

%I #16 Feb 27 2019 01:18:19

%S 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,

%T 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,

%U 1,1,2,2,2,2,2,2,1,1,1,1,1,1,2,2,2,1

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

%C a(n) is probably positive for all n > 191913030. - _Charles R Greathouse IV_, Jul 01 2011

%F Conjecturally, a(n) ~ 2*n^(1/4)/log n. - _Charles R Greathouse IV_, Jul 01 2011

%p 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

%t Table[PrimePi[n]-PrimePi[n-2*Sqrt[Sqrt[n]]],{n,90}] (* _Harvey P. Dale_, Feb 24 2018 *)

%Y Cf. A188817, A189025, A192226.

%K nonn

%O 1,3

%A _Juri-Stepan Gerasimov_, Jun 26 2011